메뉴 건너뛰기




Volumn 209, Issue 1, 1998, Pages 1-64

Identities for Classical Group Characters of Nearly Rectangular Shape

Author keywords

Characters of Lie groups; General linear characters; Littlewood Richardson rule; Orthogonal characters; Plane partitions; Restriction rules; Schur functions; Symplectic characters; Tableaux

Indexed keywords


EID: 0039835549     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1998.7531     Document Type: Article
Times cited : (43)

References (39)
  • 1
    • 51249191810 scopus 로고
    • Algebraic identities for parafermi statistics of given order
    • Bracken A. J., Green H. S. Algebraic identities for parafermi statistics of given order. Nuovo Cimento. 9A:1972;349-365.
    • (1972) Nuovo Cimento , vol.9 , pp. 349-365
    • Bracken, A.J.1    Green, H.S.2
  • 3
    • 33646921165 scopus 로고
    • Symplectic standard tableaux
    • DeConcini C. Symplectic standard tableaux. Adv. Math. 34:1979;1-27.
    • (1979) Adv. Math. , vol.34 , pp. 1-27
    • Deconcini, C.1
  • 4
    • 0000628354 scopus 로고
    • A characteristic-free approach to invariant theory
    • DeConcini C., Procesi C. A characteristic-free approach to invariant theory. Adv. Math. 21:1976;330-354.
    • (1976) Adv. Math. , vol.21 , pp. 330-354
    • Deconcini, C.1    Procesi, C.2
  • 5
    • 0030636910 scopus 로고    scopus 로고
    • Lattice path proofs for determinant formulas for symplectic and orthogonal characters
    • Fulmek M., Krattenthaler C. Lattice path proofs for determinant formulas for symplectic and orthogonal characters. J. Combin. Theory Ser. A. 77:1997;3-50.
    • (1997) J. Combin. Theory Ser. a , vol.77 , pp. 3-50
    • Fulmek, M.1    Krattenthaler, C.2
  • 7
    • 38249013077 scopus 로고
    • A linear operator for symmetric functions and tableaux in a strip with given trace
    • Goulden I. P. A linear operator for symmetric functions and tableaux in a strip with given trace. Discrete Math. 99:1992;69-77.
    • (1992) Discrete Math. , vol.99 , pp. 69-77
    • Goulden, I.P.1
  • 8
    • 38249012783 scopus 로고
    • On a bijection between Littlewood-Richardson fillings of conjugate shape
    • Hanlon Ph., Sundaram S. On a bijection between Littlewood-Richardson fillings of conjugate shape. J. Combin. Theory Ser. A. 60:1992;1-18.
    • (1992) J. Combin. Theory Ser. a , vol.60 , pp. 1-18
    • Hanlon, Ph.1    Sundaram, S.2
  • 10
    • 0001622340 scopus 로고
    • Modification rules and products of irreducible representations of the unitary, orthogonal, and symplectic groups
    • King R. C. Modification rules and products of irreducible representations of the unitary, orthogonal, and symplectic groups. J. Math. Phys. 12:1971;1588-1598.
    • (1971) J. Math. Phys. , vol.12 , pp. 1588-1598
    • King, R.C.1
  • 11
    • 0000601432 scopus 로고
    • Weight multiplicities for the classical groups
    • King R. C. Weight multiplicities for the classical groups. Lecture Notes in Phys. 50:1975;490-499.
    • (1975) Lecture Notes in Phys. , vol.50 , pp. 490-499
    • King, R.C.1
  • 12
    • 0001176796 scopus 로고
    • Branching rules for classical Lie groups using tensor and spinor methods
    • King R. C. Branching rules for classical Lie groups using tensor and spinor methods. J. Phys. A. 8:1975;429-449.
    • (1975) J. Phys. a , vol.8 , pp. 429-449
    • King, R.C.1
  • 14
    • 84972578253 scopus 로고
    • Permutations, matrices, and generalized Young tableaux
    • Knuth D. E. Permutations, matrices, and generalized Young tableaux. Pacific J. Math. 34:1970;709-727.
    • (1970) Pacific J. Math. , vol.34 , pp. 709-727
    • Knuth, D.E.1
  • 16
    • 38249020712 scopus 로고
    • Young diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank
    • Koike K., Terada I. Young diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank. Adv. Math. 79:1990;104-135.
    • (1990) Adv. Math. , vol.79 , pp. 104-135
    • Koike, K.1    Terada, I.2
  • 17
    • 0012114097 scopus 로고
    • Generating functions for shifted plane partitions
    • Krattenthaler C. Generating functions for shifted plane partitions. J. Statist. Plann. Inference. 34:1993;197-208.
    • (1993) J. Statist. Plann. Inference , vol.34 , pp. 197-208
    • Krattenthaler, C.1
  • 19
    • 0003321117 scopus 로고
    • The major counting of nonintersecting lattice paths and generating functions for tableaux
    • Krattenthaler C. The major counting of nonintersecting lattice paths and generating functions for tableaux. Mem. Amer. Math. Soc. 115:1995.
    • (1995) Mem. Amer. Math. Soc. , vol.115
    • Krattenthaler, C.1
  • 21
    • 0039843731 scopus 로고
    • Bases for fundamental representation of classical groups
    • Lakshmibai V. Bases for fundamental representation of classical groups. C. R. Acad. Paris Sér. I Math. 302:1986;387-390.
    • (1986) C. R. Acad. Paris Sér. I Math. , vol.302 , pp. 387-390
    • Lakshmibai, V.1
  • 24
    • 0001319192 scopus 로고
    • A generalization of the Littlewood-Richardson rule
    • Littelmann P. A generalization of the Littlewood-Richardson rule. J. Algebra. 130:1990;328-368.
    • (1990) J. Algebra , vol.130 , pp. 328-368
    • Littelmann, P.1
  • 27
    • 0000403467 scopus 로고    scopus 로고
    • Applications of minor summation formulas to rectangular-shaped representations of classical groups
    • S. Okada, Applications of minor summation formulas to rectangular-shaped representations of classical groups, J. Algebra.
    • J. Algebra
    • Okada, S.1
  • 28
    • 85032070245 scopus 로고
    • Shifted plane partitions of trapezoidal shape
    • Proctor R. A. Shifted plane partitions of trapezoidal shape. Proc. Amer. Math. Soc. 89:1983;553-559.
    • (1983) Proc. Amer. Math. Soc. , vol.89 , pp. 553-559
    • Proctor, R.A.1
  • 29
    • 84989135943 scopus 로고
    • Bruhat lattices, plane partition generating functions, and minuscule representations
    • Proctor R. A. Bruhat lattices, plane partition generating functions, and minuscule representations. European J. Combin. 5:1984;331-350.
    • (1984) European J. Combin. , vol.5 , pp. 331-350
    • Proctor, R.A.1
  • 30
    • 0000476307 scopus 로고
    • Odd symplectic groups
    • Proctor R. A. Odd symplectic groups. Invent. Math. 92:1988;307-332.
    • (1988) Invent. Math. , vol.92 , pp. 307-332
    • Proctor, R.A.1
  • 31
    • 85011025701 scopus 로고
    • New symmetric plane partition identities from invariant theory work of DeConcini and Procesi
    • Proctor R. A. New symmetric plane partition identities from invariant theory work of DeConcini and Procesi. European J. Combin. 11:1990;289-300.
    • (1990) European J. Combin. , vol.11 , pp. 289-300
    • Proctor, R.A.1
  • 32
    • 84951507020 scopus 로고
    • A generalized Berele-Schensted algorithm and conjectured Young tableaux for intermediate symplectic groups
    • Proctor R. A. A generalized Berele-Schensted algorithm and conjectured Young tableaux for intermediate symplectic groups. Trans. Amer. Math. Soc. 324:1991;655-692.
    • (1991) Trans. Amer. Math. Soc. , vol.324 , pp. 655-692
    • Proctor, R.A.1
  • 33
    • 38149147728 scopus 로고
    • Young tableaux, Gelfand patterns, and branching rules for classical groups
    • Proctor R. A. Young tableaux, Gelfand patterns, and branching rules for classical groups. J. Algebra. 164:1994;299-360.
    • (1994) J. Algebra , vol.164 , pp. 299-360
    • Proctor, R.A.1
  • 34
    • 0003823142 scopus 로고
    • Pacific Grove: Wadsworth and Brooks/Cole
    • Sagan B. E. The Symmetric Group. 1991;Wadsworth and Brooks/Cole, Pacific Grove.
    • (1991) The Symmetric Group
    • Sagan, B.E.1
  • 36
    • 0002566735 scopus 로고
    • Symmetries of plane partitions
    • Stanley R. P. Symmetries of plane partitions. J. Combin. Theory Ser. A. 43:1986;103-113.
    • (1986) J. Combin. Theory Ser. a , vol.43 , pp. 103-113
    • Stanley, R.P.1
  • 37
    • 0001666494 scopus 로고
    • Hall-Littlewood functions, plane partitions and the Rogers-Ramanujan identities
    • Stembridge J. R. Hall-Littlewood functions, plane partitions and the Rogers-Ramanujan identities. Trans. Amer. Math. Soc. 319:1990;469-498.
    • (1990) Trans. Amer. Math. Soc. , vol.319 , pp. 469-498
    • Stembridge, J.R.1
  • 38
    • 0002777429 scopus 로고
    • Nonintersecting paths, pfaffians and plane partitions
    • Stembridge J. R. Nonintersecting paths, pfaffians and plane partitions. Adv. Math. 83:1990;96-131.
    • (1990) Adv. Math. , vol.83 , pp. 96-131
    • Stembridge, J.R.1
  • 39
    • 0012925391 scopus 로고
    • Tableaux in the representation theory of the classical Lie groups: Invariant theory and tableaux
    • Sundaram S. Tableaux in the representation theory of the classical Lie groups: Invariant theory and tableaux. IMA Vol. Math. Appl. 19:1989;191-225.
    • (1989) IMA Vol. Math. Appl. , vol.19 , pp. 191-225
    • Sundaram, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.