메뉴 건너뛰기




Volumn 8, Issue 1, 1998, Pages 61-95

Visual basic representations: An atlas

Author keywords

Action constants; Adjoint representation; Basic representation; Bruhat order; Canonical base; Chevalley group; Crystal graph; Microweight; Multilinear invariants; Quantum group; Root systems; Semisimple Lie algebra; Weight diagram; Weyl group; Weyl modules

Indexed keywords


EID: 0032331133     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196798000053     Document Type: Article
Times cited : (62)

References (132)
  • 2
    • 38249035671 scopus 로고
    • 2 as the groups of a trilinear form
    • 2 as the groups of a trilinear form, J. Algebra 109 (1) (1987), 193-259.
    • (1987) J. Algebra , vol.109 , Issue.1 , pp. 193-259
    • Aschbacher, M.1
  • 3
    • 0007141126 scopus 로고
    • Some multilinear forms with large isometry groups
    • M. Aschbacher, Some multilinear forms with large isometry groups, Geom. dedic. 25 (1)-(3) (1988), 417-465.
    • (1988) Geom. Dedic. , vol.25 , Issue.1-3 , pp. 417-465
    • Aschbacher, M.1
  • 4
    • 84963478976 scopus 로고
    • On the structure of parabolic subgroups
    • H. Azad, M. Barry and G. M. Seitz, On the structure of parabolic subgroups, Commun. Algebra 18 (1990), 551-562.
    • (1990) Commun. Algebra , vol.18 , pp. 551-562
    • Azad, H.1    Barry, M.2    Seitz, G.M.3
  • 7
    • 0000884168 scopus 로고
    • Orderings of Coxeter groups
    • A. Björner, Orderings of Coxeter groups, Contemp. Math. 34 (1984), 175-195.
    • (1984) Contemp. Math. , vol.34 , pp. 175-195
    • Björner, A.1
  • 8
    • 0001757668 scopus 로고
    • Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings
    • A. Björner, Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings, Advances in Math. 52 (1984), 173-212.
    • (1984) Advances in Math. , vol.52 , pp. 173-212
    • Björner, A.1
  • 9
    • 0002592084 scopus 로고
    • Bruhat order of Coxeter groups and shellability
    • A. Björner and M. Wachs, Bruhat order of Coxeter groups and shellability, Adv. Math. 43 (1) (1983), 87-100.
    • (1983) Adv. Math. , vol.43 , Issue.1 , pp. 87-100
    • Björner, A.1    Wachs, M.2
  • 10
    • 84966226471 scopus 로고
    • Generalized quotients in Coxeter groups
    • A. Björner and M. Wachs, Generalized quotients in Coxeter groups, Trans. Amer. Math. Soc. 308 (1) (1988), 1-37.
    • (1988) Trans. Amer. Math. Soc. , vol.308 , Issue.1 , pp. 1-37
    • Björner, A.1    Wachs, M.2
  • 11
    • 0000591280 scopus 로고
    • A comparison theory for the structure of induced representations. I, II
    • B. D. Boe and D. H. Collingwood, A comparison theory for the structure of induced representations. I, II, J. Algebra 94 (3) (1985), 511-545; Math. Z. 190 (1) (1985), 1-11.
    • (1985) J. Algebra , vol.94 , Issue.3 , pp. 511-545
    • Boe, B.D.1    Collingwood, D.H.2
  • 12
    • 0000591280 scopus 로고
    • B. D. Boe and D. H. Collingwood, A comparison theory for the structure of induced representations. I, II, J. Algebra 94 (3) (1985), 511-545; Math. Z. 190 (1) (1985), 1-11.
    • (1985) Math. Z. , vol.190 , Issue.1 , pp. 1-11
  • 13
    • 0542425122 scopus 로고
    • A multiplicity one theorem for holomorphically induced representations
    • B. D. Boe and D. H. Collingwood, A multiplicity one theorem for holomorphically induced representations, Math. Z. 192 (1) (1986), 265-282.
    • (1986) Math. Z. , vol.192 , Issue.1 , pp. 265-282
    • Boe, B.D.1    Collingwood, D.H.2
  • 15
    • 0001019319 scopus 로고
    • Properties and linear representations of Chevalley groups
    • A. Borel, Properties and linear representations of Chevalley groups, Lecture Notes-Math., Vol. 131, 1970, pp. 1-55.
    • (1970) Lecture Notes-Math. , vol.131 , pp. 1-55
    • Borel, A.1
  • 19
    • 0001759652 scopus 로고
    • Représentations exceptionnelles des groups semisimples
    • e sér
    • e sér 18 (1985), 345-387.
    • (1985) Ann. Sci Éc Norm Sup. , vol.18 , pp. 345-387
    • Brion, M.1
  • 20
    • 0011287526 scopus 로고
    • Graphs related to exceptional root systems
    • Colloquia Mathematica Soc. János Bolyai, North Holland, Amsterdam
    • F. C. Bussemaker, D. M. Cvetkovič and J. J. Seidel, Graphs related to exceptional root systems, Combinatorics, Colloquia Mathematica Soc. János Bolyai, Vol. 18, North Holland, Amsterdam, 1978, pp. 185-191.
    • (1978) Combinatorics , vol.18 , pp. 185-191
    • Bussemaker, F.C.1    Cvetkovič, D.M.2    Seidel, J.J.3
  • 21
    • 0542377673 scopus 로고
    • Weight diagram construction of Lax operators
    • S. L. Carbon and E. J. Piard, Weight diagram construction of Lax operators, J. Math. Phys. 33 (8) (1992), 2664-2674.
    • (1992) J. Math. Phys. , vol.33 , Issue.8 , pp. 2664-2674
    • Carbon, S.L.1    Piard, E.J.2
  • 25
  • 26
    • 0001929645 scopus 로고    scopus 로고
    • Point-line spaces related to buildings
    • Chapter 12 (to appear)
    • A. M. Cohen, Point-line spaces related to buildings, Handbook of incidence geometry, Chapter 12 (to appear).
    • Handbook of Incidence Geometry
    • Cohen, A.M.1
  • 28
    • 0038889185 scopus 로고
    • Gröbner bases and standard monomial theory
    • Birchäuser, Boston
    • A. M. Cohen and R. H. Cushman, Gröbner bases and standard monomial theory, Computational Algebraic Geometry, Birchäuser, Boston, 1993, 41-61.
    • (1993) Computational Algebraic Geometry , pp. 41-61
    • Cohen, A.M.1    Cushman, R.H.2
  • 31
    • 84968468190 scopus 로고
    • Embeddings of Harish-Chandra modules, n-homology and the composition series problem
    • D. Collingwood, Embeddings of Harish-Chandra modules, n-homology and the composition series problem, Trans. Amer. Math. Soc. 285 (1984), 565-579.
    • (1984) Trans. Amer. Math. Soc. , vol.285 , pp. 565-579
    • Collingwood, D.1
  • 33
    • 85034469105 scopus 로고
    • Preprint Univ. California at Santa Cruz
    • 7. I, Preprint Univ. California at Santa Cruz (1988), 1-52.
    • (1988) 7 , vol.1 , pp. 1-52
    • Cooperstein, B.N.1
  • 35
    • 0002782280 scopus 로고
    • Geometric hyperplanes of embeddable Lie incidence geometries
    • Proc. 3rd Isle of Thorns Conf., Chelwood Gate
    • B. N. Cooperstein and E. Shult, Geometric hyperplanes of embeddable Lie incidence geometries, Adv. Finite Geom. & Designs, Proc. 3rd Isle of Thorns Conf., 1990, Chelwood Gate, 1991, pp. 81-91.
    • (1990) Adv. Finite Geom. & Designs , pp. 81-91
    • Cooperstein, B.N.1    Shult, E.2
  • 37
    • 51249189687 scopus 로고
    • Hecke algebras and characters of parabolic type of finite groups with (B,N)-pairs
    • C. W. Curtis, N. Iwahori and R. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with (B,N)-pairs, Publ. Math. Inst. Hautes Et. Sci. 40 (1971), 81-116.
    • (1971) Publ. Math. Inst. Hautes Et. Sci. , vol.40 , pp. 81-116
    • Curtis, C.W.1    Iwahori, N.2    Kilmoyer, R.3
  • 38
    • 0001146619 scopus 로고
    • Differential operators and highest weight representations
    • M. Davidson, T. Enright and R. Stanke, Differential operators and highest weight representations, Memoirs of AMS 94 (455) (1991), 1-102.
    • (1991) Memoirs of AMS , vol.94 , Issue.455 , pp. 1-102
    • Davidson, M.1    Enright, T.2    Stanke, R.3
  • 39
    • 0000781847 scopus 로고
    • Some characterisations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function
    • V. V. Deodhar, Some characterisations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function, Invent. Math. 39 (2) (1977), 187-198.
    • (1977) Invent. Math. , vol.39 , Issue.2 , pp. 187-198
    • Deodhar, V.V.1
  • 40
    • 49349131679 scopus 로고
    • On Bruhat ordering and weight lattice ordering for a Weyl group
    • V. V. Deodhar, On Bruhat ordering and weight lattice ordering for a Weyl group, Proc. Nederl. Akad. Wetensch Ser. A 40 (5) (1978), 423-435.
    • (1978) Proc. Nederl. Akad. Wetensch Ser. A , vol.40 , Issue.5 , pp. 423-435
    • Deodhar, V.V.1
  • 41
    • 0001447863 scopus 로고
    • A splitting criterion for the Bruhat orderings on Coxeter groups
    • V. V. Deodhar, A splitting criterion for the Bruhat orderings on Coxeter groups, Comm. Algebra 15 (9) (1987), 1889-1894.
    • (1987) Comm. Algebra , vol.15 , Issue.9 , pp. 1889-1894
    • Deodhar, V.V.1
  • 43
    • 0001337553 scopus 로고
    • Some properties of the weight system of a linear representation of a semi-simple Lie group
    • E. B. Dynkin, Some properties of the weight system of a linear representation of a semi-simple Lie group, Dokl. Acad. Sci. USSR 71 (1950), 221-224.
    • (1950) Dokl. Acad. Sci. USSR , vol.71 , pp. 221-224
    • Dynkin, E.B.1
  • 44
    • 0002012811 scopus 로고
    • Maximal subgroups of the classical groups
    • 2nd ser.
    • E. B. Dynkin, Maximal subgroups of the classical groups, Amer. Math. Soc. Transl, 2nd ser. 6 (1957), 245-378.
    • (1957) Amer. Math. Soc. Transl , vol.6 , pp. 245-378
    • Dynkin, E.B.1
  • 45
    • 84966261375 scopus 로고
    • Highest weight modules for Hermitian symmetric pairs of exceptional type
    • T. Enright and B. Shelton, Highest weight modules for Hermitian symmetric pairs of exceptional type, Proc. Amer. Math. Soc. 106 (1989), 807-819.
    • (1989) Proc. Amer. Math. Soc. , vol.106 , pp. 807-819
    • Enright, T.1    Shelton, B.2
  • 46
    • 0038221799 scopus 로고
    • Categories of highest weight modules: Applications to classical Hermitian symmetric pairs
    • T. Enright and B. Shelton, Categories of highest weight modules: applications to classical Hermitian symmetric pairs, Memoirs of AMS. 67 (367) (1987), 1-94.
    • (1987) Memoirs of AMS. , vol.67 , Issue.367 , pp. 1-94
    • Enright, T.1    Shelton, B.2
  • 48
    • 0003114388 scopus 로고
    • Monomorphisms and direct limits of finite groups of Lie type
    • B. Hartley and G. Shute, Monomorphisms and direct limits of finite groups of Lie type, Quart. J. Math. 35 (1) (1984), 49-71.
    • (1984) Quart. J. Math. , vol.35 , Issue.1 , pp. 49-71
    • Hartley, B.1    Shute, G.2
  • 49
    • 25044436550 scopus 로고
    • Groupes de Chevalley et groupes classiques
    • J.-Y. Hée, Groupes de Chevalley et groupes classiques, Publ. Math. Univ. Paris VII 17 (1984), 1-54.
    • (1984) Publ. Math. Univ. Paris VII , vol.17 , pp. 1-54
    • Hée, J.-Y.1
  • 51
    • 51249181382 scopus 로고
    • Combinatorics and intersections of Schubert varieties
    • H. Hiller, Combinatorics and intersections of Schubert varieties, Comm. Math. Helv. 57 (1) (1982), 41-59.
    • (1982) Comm. Math. Helv. , vol.57 , Issue.1 , pp. 41-59
    • Hiller, H.1
  • 52
    • 0002640111 scopus 로고
    • Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond
    • R. Howe, Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond, Israel Math. Conf. Proc. 8 (1995), 1-182.
    • (1995) Israel Math. Conf. Proc. , vol.8 , pp. 1-182
    • Howe, R.1
  • 56
    • 84967728446 scopus 로고
    • Protective modules in the category Os: Self-duality
    • R. S. Irving, Protective modules in the category Os: Self-duality, Trans. Amer. Math. Soc. 291 (2) (1985), 701-732.
    • (1985) Trans. Amer. Math. Soc. , vol.291 , Issue.2 , pp. 701-732
    • Irving, R.S.1
  • 58
    • 0001065787 scopus 로고    scopus 로고
    • Lectures on Quantum Groups
    • Providence, R.I.
    • J. C. Jantzen, Lectures on Quantum Groups, Amer. Math. Soc., Providence, R.I., 1996.
    • (1996) Amer. Math. Soc.
    • Jantzen, J.C.1
  • 59
    • 0002163296 scopus 로고
    • On the 1-cohomology of finite groups of Lie type
    • Park City, Utah- Academic Press, N.Y.
    • W. Jones and B. Parshall, On the 1-cohomology of finite groups of Lie type, Proc. Conf. Finite Groups (Park City, Utah-1975), Academic Press, N.Y., 1976, pp. 313-328.
    • (1975) Proc. Conf. Finite Groups , pp. 313-328
    • Jones, W.1    Parshall, B.2
  • 61
    • 34249963938 scopus 로고
    • Crystallizing the q-analogue of universal enveloping algebra
    • M. Kashiwara, Crystallizing the q-analogue of universal enveloping algebra, Comm. Math. Phys. 133 (1990), 249-260.
    • (1990) Comm. Math. Phys. , vol.133 , pp. 249-260
    • Kashiwara, M.1
  • 62
    • 84974000954 scopus 로고
    • On crystal base of q-analogue of universal enveloping algebras
    • M. Kashiwara, On crystal base of q-analogue of universal enveloping algebras, Duke Math. J. 63 (1991), 456-516.
    • (1991) Duke Math. J. , vol.63 , pp. 456-516
    • Kashiwara, M.1
  • 63
    • 0000871764 scopus 로고
    • Crystal graphs for representations of the q-analogue of classical Lie algebras
    • M. Kashiwara and T. Nakashima, Crystal graphs for representations of the q-analogue of classical Lie algebras, J. Algebra 165 (1994), 295-345.
    • (1994) J. Algebra , vol.165 , pp. 295-345
    • Kashiwara, M.1    Nakashima, T.2
  • 64
    • 0542425131 scopus 로고
    • Schubert varieties and standard monomial theory
    • PWN, Warsaw
    • V. Lakshmibai, Schubert varieties and standard monomial theory, Topics in Algebra, Part 2, PWN, Warsaw, 1990, pp. 365-378.
    • (1990) Topics in Algebra , Issue.2 PART , pp. 365-378
    • Lakshmibai, V.1
  • 67
    • 38249016479 scopus 로고
    • Multiplicities of points on a Schubert variety in a minuscule G/P
    • V. Lakshmibai and J. Weyman, Multiplicities of points on a Schubert variety in a minuscule G/P, Adv. Math. 84 (2) (1990), 179-208.
    • (1990) Adv. Math. , vol.84 , Issue.2 , pp. 179-208
    • Lakshmibai, V.1    Weyman, J.2
  • 69
    • 84966213581 scopus 로고
    • A system of quadrics describing the orbit of the highest weight vector
    • W. Lichtenstein, A system of quadrics describing the orbit of the highest weight vector, Proc. Amer. Math. Soc. 84 (4) (1982), 605-608.
    • (1982) Proc. Amer. Math. Soc. , vol.84 , Issue.4 , pp. 605-608
    • Lichtenstein, W.1
  • 70
    • 0000049326 scopus 로고
    • A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras
    • P. Littelmann, A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras, Invent. Math. 116 (1994), 229-246.
    • (1994) Invent. Math. , vol.116 , pp. 229-246
    • Littelmann, P.1
  • 71
    • 0002596308 scopus 로고
    • Crystal graphs and Young tableau
    • P. Littelmann, Crystal graphs and Young tableau, J. Algebra 175 (1) (1995), 65-87.
    • (1995) J. Algebra , vol.175 , Issue.1 , pp. 65-87
    • Littelmann, P.1
  • 72
    • 21844525391 scopus 로고
    • Path and root operators in representation theory
    • P. Littelmann, Path and root operators in representation theory, Ann. Math. 142 (1995), 499-525.
    • (1995) Ann. Math. , vol.142 , pp. 499-525
    • Littelmann, P.1
  • 73
    • 84968495738 scopus 로고
    • Canonical bases arising from quantized enveloping algebras
    • G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), 447-498.
    • (1990) J. Amer. Math. Soc. , vol.3 , pp. 447-498
    • Lusztig, G.1
  • 74
    • 0003360864 scopus 로고
    • Canonical bases arising from quantized enveloping algebras. II
    • G. Lusztig, Canonical bases arising from quantized enveloping algebras. II, Progress Theor. Physics 102 (1990), 175-202.
    • (1990) Progress Theor. Physics , vol.102 , pp. 175-202
    • Lusztig, G.1
  • 76
    • 0030171094 scopus 로고    scopus 로고
    • An algebraic-geometric parametrization of the canonical basis
    • G. Lusztig, An algebraic-geometric parametrization of the canonical basis, Adv. Math. 120 (1) (1996), 173-190.
    • (1996) Adv. Math. , vol.120 , Issue.1 , pp. 173-190
    • Lusztig, G.1
  • 77
    • 0039280072 scopus 로고
    • Les nombres de Tamagawa de certains groupes exceptionnels
    • J. G. M. Mars, Les nombres de Tamagawa de certains groupes exceptionnels, Bull. Soc. Math. France 94 (1966), 97-140.
    • (1966) Bull. Soc. Math. France , vol.94 , pp. 97-140
    • Mars, J.G.M.1
  • 79
    • 25044480138 scopus 로고
    • Bases des représentations des groupes simples complexes (d'apres Kashiwara, Lusztig, Ringel et al.)
    • O. Mathieu, Bases des représentations des groupes simples complexes (d'apres Kashiwara, Lusztig, Ringel et al.), Asterisque (1991), no. 201-203, 421-442.
    • (1991) Asterisque , vol.201-203 , pp. 421-442
    • Mathieu, O.1
  • 84
    • 85034463668 scopus 로고
    • Chevalley-Matsumoto decomposition for twisted Chevalley groups
    • Riga Univ. Press, Riga, (in Russian)
    • E. B. Plotkin, Chevalley-Matsumoto decomposition for twisted Chevalley groups, Topological spaces and their maps, Riga Univ. Press, Riga, 1985, pp. 64-73 (in Russian).
    • (1985) Topological Spaces and Their Maps , pp. 64-73
    • Plotkin, E.B.1
  • 85
    • 0542401280 scopus 로고
    • Ph. D. Thesis, Leningrad State University, (in Russian)
    • 1-functor, Ph. D. Thesis, Leningrad State University, 1985, pp. 1-118 (in Russian).
    • (1985) 1-functor , pp. 1-118
    • Plotkin, E.B.1
  • 87
    • 0038889181 scopus 로고
    • 1-functor for some exceptional Chevalley groups
    • 1-functor for some exceptional Chevalley groups, J. Soviet. Math (1) (1993), 751-767.
    • (1993) J. Soviet. Math , Issue.1 , pp. 751-767
    • Plotkin, E.B.1
  • 89
    • 0001759474 scopus 로고
    • Classical Bruhat orders and lexicographic shellability
    • R. A. Proctor, Classical Bruhat orders and lexicographic shellability, J. Algebra 77 (1) (1982), 104-126.
    • (1982) J. Algebra , vol.77 , Issue.1 , pp. 104-126
    • Proctor, R.A.1
  • 90
    • 84989135943 scopus 로고
    • Bruhat lattices, plane partition generating functions, and minuscule representations
    • R. A. Proctor, Bruhat lattices, plane partition generating functions, and minuscule representations, Europ. J. Combinatorics 5 (1984), 331-350.
    • (1984) Europ. J. Combinatorics , vol.5 , pp. 331-350
    • Proctor, R.A.1
  • 91
    • 38249040265 scopus 로고
    • A Dynkin diagram classification theorem arising from a combinatorial problem
    • R. A. Proctor, A Dynkin diagram classification theorem arising from a combinatorial problem, Adv. Math. 62 (2) (1986), 103-117.
    • (1986) Adv. Math. , vol.62 , Issue.2 , pp. 103-117
    • Proctor, R.A.1
  • 92
    • 0001025240 scopus 로고
    • Finiteness theorems for orbits of algebraic groups
    • R. Richardson, Finiteness theorems for orbits of algebraic groups, Indag. Math. 88 (1985), 337-344.
    • (1985) Indag. Math. , vol.88 , pp. 337-344
    • Richardson, R.1
  • 93
    • 0000386670 scopus 로고
    • Parabolic subgroups with abelian unipotent radical
    • R. Richardson, G. E. Röhrle and R. Steinberg, Parabolic subgroups with abelian unipotent radical, Invent. Math. 110 (3) (1992), 649-671.
    • (1992) Invent. Math. , vol.110 , Issue.3 , pp. 649-671
    • Richardson, R.1    Röhrle, G.E.2    Steinberg, R.3
  • 94
    • 0000363223 scopus 로고
    • The Bruhat order on symmetric varieties
    • R. W. Richardson and T. A. Springer, The Bruhat order on symmetric varieties, Geom. dedic. 35 (1990), 389-436.
    • (1990) Geom. Dedic. , vol.35 , pp. 389-436
    • Richardson, R.W.1    Springer, T.A.2
  • 95
    • 0542377604 scopus 로고
    • Combinatorics and geometry of K-orbits on the flag manifold
    • Australian National University
    • R. W. Richardson and T. A. Springer, Combinatorics and geometry of K-orbits on the flag manifold, Report Centre for Math. Analysis, Australian National University 222 (1992).
    • (1992) Report Centre for Math. Analysis , vol.222
    • Richardson, R.W.1    Springer, T.A.2
  • 96
    • 0003063030 scopus 로고
    • Representation theory of finite-dimensional algebras
    • (Durham-1985), Cambridge Univ. Press
    • C. M. Ringel, Representation theory of finite-dimensional algebras, Representations of Algebras (Durham-1985), Cambridge Univ. Press, 1986, pp. 7-79.
    • (1986) Representations of Algebras , pp. 7-79
    • Ringel, C.M.1
  • 97
    • 85009764731 scopus 로고
    • Orbits in internal Chevalley modules
    • (Durham-1990), Cambridge Univ. Press
    • G. E. Röhrle, Orbits in internal Chevalley modules, Groups, Combinatorics and Geometry (Durham-1990), Cambridge Univ. Press, 1992, pp. 311-315.
    • (1992) Groups, Combinatorics and Geometry , pp. 311-315
    • Röhrle, G.E.1
  • 98
    • 38249003172 scopus 로고
    • On the structure of parabolic subgroups in algebraic groups
    • G. E. Röhrle, On the structure of parabolic subgroups in algebraic groups, J. Algebra 157 (1) (1993), 80-115.
    • (1993) J. Algebra , vol.157 , Issue.1 , pp. 80-115
    • Röhrle, G.E.1
  • 99
    • 0001257257 scopus 로고
    • On extraspecial parabolic subgroups
    • G. E. Röhrle, On extraspecial parabolic subgroups, Contemp. Math. 153 (1993), 143-155.
    • (1993) Contemp. Math. , vol.153 , pp. 143-155
    • Röhrle, G.E.1
  • 100
    • 0000622934 scopus 로고
    • Sheaves on buildings and modular representations of Chevalley groups
    • M. A. Ronan and S. D. Smith, Sheaves on buildings and modular representations of Chevalley groups, J. Algebra 96 (2) (1985), 319-346.
    • (1985) J. Algebra , vol.96 , Issue.2 , pp. 319-346
    • Ronan, M.A.1    Smith, S.D.2
  • 101
    • 85034464020 scopus 로고
    • Preprint Universität Bielefeld
    • R. Scharlau, Buildings, Preprint Universität Bielefeld (1993), no. 16, 1-129.
    • (1993) Buildings , vol.16 , pp. 1-129
    • Scharlau, R.1
  • 102
    • 0003275047 scopus 로고
    • Maximal subgroups of classical algebraic groups
    • G. M. Seitz, Maximal subgroups of classical algebraic groups, Mem. Amer. Math. Soc. 67 (365) (1987), 1-286.
    • (1987) Mem. Amer. Math. Soc. , vol.67 , Issue.365 , pp. 1-286
    • Seitz, G.M.1
  • 104
    • 0542425137 scopus 로고
    • Semisimple root elements of Chevalley groups
    • A. Semenov and N. A. Vavilov, Semisimple root elements of Chevalley groups, Russian Math. Doklady 50 (2) (1995), 325-329 (see also; Halbeinfache Wurzelelemente in Chevalley-Gruppen, Preprint Universität Bielefeld (1994), no. 2, 1-11.
    • (1995) Russian Math. Doklady , vol.50 , Issue.2 , pp. 325-329
    • Semenov, A.1    Vavilov, N.A.2
  • 105
    • 85034464949 scopus 로고
    • Preprint Universität Bielefeld
    • A. Semenov and N. A. Vavilov, Semisimple root elements of Chevalley groups, Russian Math. Doklady 50 (2) (1995), 325-329 (see also; Halbeinfache Wurzelelemente in Chevalley-Gruppen, Preprint Universität Bielefeld (1994), no. 2, 1-11.
    • (1994) Halbeinfache Wurzelelemente in Chevalley-Gruppen , vol.2 , pp. 1-11
  • 107
    • 0542448913 scopus 로고
    • The work of P.Littelmann and standard monomial theory
    • Narosa, New Delhi
    • C. S. Seshadri, The work of P.Littelmann and standard monomial theory, Current trends in Mathematics and Physics, Narosa, New Delhi, 1995, pp. 178-197.
    • (1995) Current Trends in Mathematics and Physics , pp. 178-197
    • Seshadri, C.S.1
  • 109
    • 0542425190 scopus 로고
    • Linear Algebraic Groups
    • in Russian, English translation to appear in Springer
    • T. A. Springer, Linear Algebraic Groups, Fundam. Trends in Math. 55 (1989), 5-136, (in Russian, English translation to appear in Springer).
    • (1989) Fundam. Trends in Math. , vol.55 , pp. 5-136
    • Springer, T.A.1
  • 110
    • 0000946102 scopus 로고
    • Weyl groups, the hard Lefschetz theorem, and the Sperner property
    • R. P. Stanley, Weyl groups, the hard Lefschetz theorem, and the Sperner property, SIAM J. Alg. Discr. Methods 1 (1980), 168-184.
    • (1980) SIAM J. Alg. Discr. Methods , vol.1 , pp. 168-184
    • Stanley, R.P.1
  • 111
    • 0038889126 scopus 로고
    • Matsumoto's solution of the congruence subgroup problem and stability theorems in algebraic K-theory
    • M. R. Stein, Matsumoto's solution of the congruence subgroup problem and stability theorems in algebraic K-theory, Proc. 19th Meeting Algebra Section Math. Soc. Japan, 1983, pp. 32-44.
    • (1983) Proc. 19th Meeting Algebra Section Math. Soc. Japan , pp. 32-44
    • Stein, M.R.1
  • 112
    • 85009800968 scopus 로고
    • 2 and related functors modeled on Chevalley groups
    • 2 and related functors modeled on Chevalley groups, Japan J. Math. 4 (1) (1978), 77-108.
    • (1978) Japan J. Math. , vol.4 , Issue.1 , pp. 77-108
    • Stein, M.R.1
  • 114
    • 84974002530 scopus 로고
    • On minuscule representations, plane partitions and involutions in complex Lie groups
    • J. R. Stembridge, On minuscule representations, plane partitions and involutions in complex Lie groups, Duke J. Math. 73 (2) (1994), 469-490.
    • (1994) Duke J. Math. , vol.73 , Issue.2 , pp. 469-490
    • Stembridge, J.R.1
  • 116
    • 0040875696 scopus 로고
    • Dr. Sci. Thesis (Habilitationschrift), Leningrad State Univ., (in Russian)
    • N. A. Vavilov, Subgroups of split classical groups, Dr. Sci. Thesis (Habilitationschrift), Leningrad State Univ., 1987, pp. 1-334 (in Russian).
    • (1987) Subgroups of Split Classical Groups , pp. 1-334
    • Vavilov, N.A.1
  • 117
    • 0542425192 scopus 로고
    • Bruhat decomposition of the semisimple long root elements in Chevalley groups
    • Leningrad Univ. Press, (in Russian)
    • N. A. Vavilov, Bruhat decomposition of the semisimple long root elements in Chevalley groups, Rings and Modules. Limit theorems of probability theory, II, Leningrad Univ. Press, 1988, pp. 18-39 (in Russian).
    • (1988) Rings and Modules. Limit Theorems of Probability Theory , vol.2 , pp. 18-39
    • Vavilov, N.A.1
  • 118
    • 0041774427 scopus 로고
    • Subgroups of Chevalley groups containing a maximal torus
    • N. A. Vavilov, Subgroups of Chevalley groups containing a maximal torus, Amer. Math. Soc. Transl. 155 (1993), 59-100.
    • (1993) Amer. Math. Soc. Transl. , vol.155 , pp. 59-100
    • Vavilov, N.A.1
  • 119
    • 0038889133 scopus 로고
    • Structure of Chevalley groups over commutative rings
    • (Hiroshima-1990), World Scientific, London
    • N. Vavilov, Structure of Chevalley groups over commutative rings, Proc. Conf. Non-Associative Algebras and Related Topics (Hiroshima-1990), World Scientific, London, 1991, pp. 219-335.
    • (1991) Proc. Conf. Non-Associative Algebras and Related Topics , pp. 219-335
    • Vavilov, N.1
  • 120
    • 0012009851 scopus 로고
    • Intermediate subgroups in Chevalley groups
    • (Como-1993), Cambridge Univ. Press
    • N. A. Vavilov, Intermediate subgroups in Chevalley groups, Proc. Conf. Groups of Lie Type and their Geometries (Como-1993), Cambridge Univ. Press, 1995, pp. 233-280.
    • (1995) Proc. Conf. Groups of Lie Type and Their Geometries , pp. 233-280
    • Vavilov, N.A.1
  • 122
  • 123
    • 0040667188 scopus 로고    scopus 로고
    • Preprint Newton Inst Math. Sci., Cambridge
    • N. A. Vavilov, The ubiquity of microweights, Preprint Newton Inst Math. Sci., Cambridge (1997), 1-56.
    • (1997) The Ubiquity of Microweights , pp. 1-56
    • Vavilov, N.A.1
  • 125
    • 0542377666 scopus 로고
    • Net subgroups of Chevalley groups. I, II
    • N. A. Vavilov and E. B. Plotkin, Net subgroups of Chevalley groups. I, II, J. Sov. Math. 19 (1) (1982), 1000-1006; 27 (4) (1984), 2874-2885.
    • (1982) J. Sov. Math. , vol.19 , Issue.1 , pp. 1000-1006
    • Vavilov, N.A.1    Plotkin, E.B.2
  • 126
    • 0039106638 scopus 로고
    • N. A. Vavilov and E. B. Plotkin, Net subgroups of Chevalley groups. I, II, J. Sov. Math. 19 (1) (1982), 1000-1006; 27 (4) (1984), 2874-2885.
    • (1984) J. Sov. Math. , vol.27 , Issue.4 , pp. 2874-2885
  • 127
    • 0013203661 scopus 로고    scopus 로고
    • Chevalley groups over commutative rings. I. Elementary calculations
    • N. A. Vavilov and E. B. Plotkin, Chevalley groups over commutative rings. I. Elementary calculations, Acta Applicandae Math. 45 (1) (1996), 73-113.
    • (1996) Acta Applicandae Math. , vol.45 , Issue.1 , pp. 73-113
    • Vavilov, N.A.1    Plotkin, E.B.2
  • 129
    • 0039097492 scopus 로고
    • Calculations in Chevalley groups over commutative rings
    • N. A. Vavilov, E. B. Plotkin and A. V. Stepanov, Calculations in Chevalley groups over commutative rings, Soviet Math. Doklady 40 (1) (1990), 145-147.
    • (1990) Soviet Math. Doklady , vol.40 , Issue.1 , pp. 145-147
    • Vavilov, N.A.1    Plotkin, E.B.2    Stepanov, A.V.3
  • 131
  • 132
    • 0000393838 scopus 로고
    • Weights of semi-simple Lie algebras on the cohomology of algebraic varieties
    • Yu. G. Zarhin, Weights of semi-simple Lie algebras on the cohomology of algebraic varieties, Izv. Akad. Nauk U.S.S.R. 48 (2) (1984), 264-304.
    • (1984) Izv. Akad. Nauk U.S.S.R. , vol.48 , Issue.2 , pp. 264-304
    • Zarhin, Yu.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.