메뉴 건너뛰기




Volumn 195, Issue 3, 1998, Pages 525-547

Structure and representations of the quantum general linear supergroup

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0032370427     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050401     Document Type: Article
Times cited : (44)

References (40)
  • 3
    • 0002510281 scopus 로고
    • Chaichian, M. and Kulish, P.P.: Phys. Lett. B234, 72 (1990); Floreanini, R., Spiridonov, V.P. and Vinet, L.: Commun. Math. Phys. 137, 149 (1991); Scheunert, M.: Serre-type relations for special linear Lie superalgebras. Lett. Math. Phys. 34, 320 (1993); Yamane, H.: A Serre type theorem for affine Lie superalgebras and their quantized universal enveloping superalgebras. Proc. Japan Acad. bf A70, 31 (1994)
    • (1990) Phys. Lett. , vol.B234 , pp. 72
    • Chaichian, M.1    Kulish, P.P.2
  • 4
    • 33645606537 scopus 로고
    • Chaichian, M. and Kulish, P.P.: Phys. Lett. B234, 72 (1990); Floreanini, R., Spiridonov, V.P. and Vinet, L.: Commun. Math. Phys. 137, 149 (1991); Scheunert, M.: Serre-type relations for special linear Lie superalgebras. Lett. Math. Phys. 34, 320 (1993); Yamane, H.: A Serre type theorem for affine Lie superalgebras and their quantized universal enveloping superalgebras. Proc. Japan Acad. bf A70, 31 (1994)
    • (1991) Commun. Math. Phys. , vol.137 , pp. 149
    • Floreanini, R.1    Spiridonov, V.P.2    Vinet, L.3
  • 5
    • 36449009718 scopus 로고
    • Serre-type relations for special linear Lie superalgebras
    • Chaichian, M. and Kulish, P.P.: Phys. Lett. B234, 72 (1990); Floreanini, R., Spiridonov, V.P. and Vinet, L.: Commun. Math. Phys. 137, 149 (1991); Scheunert, M.: Serre-type relations for special linear Lie superalgebras. Lett. Math. Phys. 34, 320 (1993); Yamane, H.: A Serre type theorem for affine Lie superalgebras and their quantized universal enveloping superalgebras. Proc. Japan Acad. bf A70, 31 (1994)
    • (1993) Lett. Math. Phys. , vol.34 , pp. 320
    • Scheunert, M.1
  • 6
    • 0002510281 scopus 로고
    • A Serre type theorem for affine Lie superalgebras and their quantized universal enveloping superalgebras
    • Chaichian, M. and Kulish, P.P.: Phys. Lett. B234, 72 (1990); Floreanini, R., Spiridonov, V.P. and Vinet, L.: Commun. Math. Phys. 137, 149 (1991); Scheunert, M.: Serre-type relations for special linear Lie superalgebras. Lett. Math. Phys. 34, 320 (1993); Yamane, H.: A Serre type theorem for affine Lie superalgebras and their quantized universal enveloping superalgebras. Proc. Japan Acad. bf A70, 31 (1994)
    • (1994) Proc. Japan Acad. bf , vol.A70 , pp. 31
    • Yamane, H.1
  • 7
    • 0000481618 scopus 로고
    • Quantum groups
    • Drinfeld, V.G.: Quantum groups. Proc. Internl. Cong. Math., Berkeley, 1, 789 (1986); Jimbo, M.: A q-difference analog of U(g) and the Yang-Baxter equation. Lett. Math. Phys., 10, 63 (1985)
    • (1986) Proc. Internl. Cong. Math., Berkeley , vol.1 , pp. 789
    • Drinfeld, V.G.1
  • 8
    • 0040323775 scopus 로고
    • A q-difference analog of U(g) and the Yang-Baxter equation
    • Drinfeld, V.G.: Quantum groups. Proc. Internl. Cong. Math., Berkeley, 1, 789 (1986); Jimbo, M.: A q-difference analog of U(g) and the Yang-Baxter equation. Lett. Math. Phys., 10, 63 (1985)
    • (1985) Lett. Math. Phys. , vol.10 , pp. 63
    • Jimbo, M.1
  • 9
    • 0001092170 scopus 로고
    • Perk, J.H.H. and Schultz, C.L.: Phys. Lett. A84, 407 (1981); Bazhanov, V.V. and Shadrikov, A.G.: Theor. Math. Phys. 73, 1302 (1987)
    • (1981) Phys. Lett. , vol.A84 , pp. 407
    • Perk, J.H.H.1    Schultz, C.L.2
  • 11
    • 84971761808 scopus 로고
    • Quantum double construction for graded Hopf algebras
    • Gould, M.D., Zhang, R.B. and Bracken, A.J.: Quantum double construction for graded Hopf algebras. Bull. Australian Math. Soc. 47, 353-375 (1993); Yamane, H.: Universal R-matrices for quantum groups associated to Lie superalgebras. Proc. Japan. Acad. bf A67, 108 (1991); Khoroshkin, S.M. and Tolstoy, V.N.: Universal R-matrix for quantized (super)algebras. Commun. Math. Phys. 141, 599 (1991)
    • (1993) Bull. Australian Math. Soc. , vol.47 , pp. 353-375
    • Gould, M.D.1    Zhang, R.B.2    Bracken, A.J.3
  • 12
    • 84971761808 scopus 로고
    • Universal R-matrices for quantum groups associated to Lie superalgebras
    • Gould, M.D., Zhang, R.B. and Bracken, A.J.: Quantum double construction for graded Hopf algebras. Bull. Australian Math. Soc. 47, 353-375 (1993); Yamane, H.: Universal R-matrices for quantum groups associated to Lie superalgebras. Proc. Japan. Acad. bf A67, 108 (1991); Khoroshkin, S.M. and Tolstoy, V.N.: Universal R-matrix for quantized (super)algebras. Commun. Math. Phys. 141, 599 (1991)
    • (1991) Proc. Japan. Acad. bf , vol.A67 , pp. 108
    • Yamane, H.1
  • 13
    • 0000457350 scopus 로고
    • Universal R-matrix for quantized (super)algebras
    • Gould, M.D., Zhang, R.B. and Bracken, A.J.: Quantum double construction for graded Hopf algebras. Bull. Australian Math. Soc. 47, 353-375 (1993); Yamane, H.: Universal R-matrices for quantum groups associated to Lie superalgebras. Proc. Japan. Acad. bf A67, 108 (1991); Khoroshkin, S.M. and Tolstoy, V.N.: Universal R-matrix for quantized (super)algebras. Commun. Math. Phys. 141, 599 (1991)
    • (1991) Commun. Math. Phys. , vol.141 , pp. 599
    • Khoroshkin, S.M.1    Tolstoy, V.N.2
  • 14
  • 15
    • 21344486553 scopus 로고
    • q(C(n)) at arbitrary q
    • q(C(n)) at arbitrary q. J. Phys. A26, 7041-7059 (1993); Palev, T.D., Stoilova, N.I. and Van der Jeugt, J.: Finite-dimensional representations of the quantum superalgebra Uq[gl(m|n)] and related q-identities. Commun. Math. Phys. 166, 367 (1994); Zhang, R.B.: The gl(M|N) super Yangian and its finite dimensional representations. Lett. Math. Phys. 37, 419-434 (1996); Zhang, R.B.: Symmetrizable quantum affine superalgebras and their representations. J. Math. Phys. 38, 535 (1997)
    • (1993) J. Phys. , vol.A26 , pp. 7041-7059
    • Zhang, R.B.1
  • 16
    • 0001105134 scopus 로고
    • Finite-dimensional representations of the quantum superalgebra Uq[gl(m|n)] and related q-identities
    • q(C(n)) at arbitrary q. J. Phys. A26, 7041-7059 (1993); Palev, T.D., Stoilova, N.I. and Van der Jeugt, J.: Finite-dimensional representations of the quantum superalgebra Uq[gl(m|n)] and related q-identities. Commun. Math. Phys. 166, 367 (1994); Zhang, R.B.: The gl(M|N) super Yangian and its finite dimensional representations. Lett. Math. Phys. 37, 419-434 (1996); Zhang, R.B.: Symmetrizable quantum affine superalgebras and their representations. J. Math. Phys. 38, 535 (1997)
    • (1994) Commun. Math. Phys. , vol.166 , pp. 367
    • Palev, T.D.1    Stoilova, N.I.2    Van Der Jeugt, J.3
  • 17
    • 0000377236 scopus 로고    scopus 로고
    • The gl(M|N) super Yangian and its finite dimensional representations
    • q(C(n)) at arbitrary q. J. Phys. A26, 7041-7059 (1993); Palev, T.D., Stoilova, N.I. and Van der Jeugt, J.: Finite-dimensional representations of the quantum superalgebra Uq[gl(m|n)] and related q-identities. Commun. Math. Phys. 166, 367 (1994); Zhang, R.B.: The gl(M|N) super Yangian and its finite dimensional representations. Lett. Math. Phys. 37, 419-434 (1996); Zhang, R.B.: Symmetrizable quantum affine superalgebras and their representations. J. Math. Phys. 38, 535 (1997)
    • (1996) Lett. Math. Phys. , vol.37 , pp. 419-434
    • Zhang, R.B.1
  • 18
    • 0031282739 scopus 로고    scopus 로고
    • Symmetrizable quantum affine superalgebras and their representations
    • q(C(n)) at arbitrary q. J. Phys. A26, 7041-7059 (1993); Palev, T.D., Stoilova, N.I. and Van der Jeugt, J.: Finite-dimensional representations of the quantum superalgebra Uq[gl(m|n)] and related q-identities. Commun. Math. Phys. 166, 367 (1994); Zhang, R.B.: The gl(M|N) super Yangian and its finite dimensional representations. Lett. Math. Phys. 37, 419-434 (1996); Zhang, R.B.: Symmetrizable quantum affine superalgebras and their representations. J. Math. Phys. 38, 535 (1997)
    • (1997) J. Math. Phys. , vol.38 , pp. 535
    • Zhang, R.B.1
  • 19
    • 21844502991 scopus 로고
    • Solutions to the quantum Yang-Baxter equation with extra non-additive parameters
    • Bracken, A.J., Gould, M.D., Zhang, Y.Z. and Delius, G.W.: Solutions to the quantum Yang-Baxter equation with extra non-additive parameters. J. Phys. 27 A, 6551-6561 (1994); Bracken, A.J., Gould, M.D., Links, J.R. and Zhang, Y.Z.: A new supersymmetric and exactly solvable model of correlated electrons Phys. Rev. Lett. 74, 2768-2771 (1995)
    • (1994) J. Phys. , vol.27 A , pp. 6551-6561
    • Bracken, A.J.1    Gould, M.D.2    Zhang, Y.Z.3    Delius, G.W.4
  • 20
    • 0001606037 scopus 로고
    • A new supersymmetric and exactly solvable model of correlated electrons
    • Bracken, A.J., Gould, M.D., Zhang, Y.Z. and Delius, G.W.: Solutions to the quantum Yang-Baxter equation with extra non-additive parameters. J. Phys. 27 A, 6551-6561 (1994); Bracken, A.J., Gould, M.D., Links, J.R. and Zhang, Y.Z.: A new supersymmetric and exactly solvable model of correlated electrons Phys. Rev. Lett. 74, 2768-2771 (1995)
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 2768-2771
    • Bracken, A.J.1    Gould, M.D.2    Links, J.R.3    Zhang, Y.Z.4
  • 21
    • 21144467652 scopus 로고
    • Braid group representations arising from quantum supergroups with arbitrary q and link polynomials
    • Zhang, R.B.: Braid group representations arising from quantum supergroups with arbitrary q and link polynomials. J. Math. Phys. 33, 3918-3930 (1992); Gould, M.D., Tsohantjis, I. and Bracken, A.J.: Quantum supergroups and link polynomials. Rev. Math. Phys. 15, 533-549 (1993); Links, J.R., Gould, and Zhang, R.B.: Quantum supergroups, link polynomials and representations of the braid generators. Rev. Math. Phys., 5, 345-361 (1993)
    • (1992) J. Math. Phys. , vol.33 , pp. 3918-3930
    • Zhang, R.B.1
  • 22
    • 21144467652 scopus 로고
    • Quantum supergroups and link polynomials
    • Zhang, R.B.: Braid group representations arising from quantum supergroups with arbitrary q and link polynomials. J. Math. Phys. 33, 3918-3930 (1992); Gould, M.D., Tsohantjis, I. and Bracken, A.J.: Quantum supergroups and link polynomials. Rev. Math. Phys. 15, 533-549 (1993); Links, J.R., Gould, and Zhang, R.B.: Quantum supergroups, link polynomials and representations of the braid generators. Rev. Math. Phys., 5, 345-361 (1993)
    • (1993) Rev. Math. Phys. , vol.15 , pp. 533-549
    • Gould, M.D.1    Tsohantjis, I.2    Bracken, A.J.3
  • 23
    • 21144467652 scopus 로고
    • Quantum supergroups, link polynomials and representations of the braid generators
    • Zhang, R.B.: Braid group representations arising from quantum supergroups with arbitrary q and link polynomials. J. Math. Phys. 33, 3918-3930 (1992); Gould, M.D., Tsohantjis, I. and Bracken, A.J.: Quantum supergroups and link polynomials. Rev. Math. Phys. 15, 533-549 (1993); Links, J.R., Gould, and Zhang, R.B.: Quantum supergroups, link polynomials and representations of the braid generators. Rev. Math. Phys., 5, 345-361 (1993)
    • (1993) Rev. Math. Phys. , vol.5 , pp. 345-361
    • Links, J.R.1    Gould2    Zhang, R.B.3
  • 24
    • 0000069384 scopus 로고
    • Quantum supergroups and topological invariants of three-manifolds
    • Zhang, R.B.: Quantum supergroups and topological invariants of three-manifolds. Rev. Math. Phys. 7, 809-831 (1995); Zhang, R.B. and Lee, H.C.: Lickorish invariant and quantum OSP(1|2). Mod. Phys. Lett. A 11, 2397 (1996)
    • (1995) Rev. Math. Phys. , vol.7 , pp. 809-831
    • Zhang, R.B.1
  • 25
    • 0000416282 scopus 로고    scopus 로고
    • Lickorish invariant and quantum OSP(1|2)
    • Zhang, R.B.: Quantum supergroups and topological invariants of three-manifolds. Rev. Math. Phys. 7, 809-831 (1995); Zhang, R.B. and Lee, H.C.: Lickorish invariant and quantum OSP(1|2). Mod. Phys. Lett. A 11, 2397 (1996)
    • (1996) Mod. Phys. Lett. A , vol.11 , pp. 2397
    • Zhang, R.B.1    Lee, H.C.2
  • 26
    • 1542483491 scopus 로고
    • Compact matrix pseudo groups
    • Woronowicz, S.L.: Compact matrix pseudo groups. Commun. Math. Phys. 111, 613 (1987); Faddeev, L.D., Reshetikhin, N.Yu. and Takhtajan, L.A.: Quantization of Lie groups and Lie algebras. Leningrad Math. J. 1, 193 (1990)
    • (1987) Commun. Math. Phys. , vol.111 , pp. 613
    • Woronowicz, S.L.1
  • 27
    • 1542483491 scopus 로고
    • Quantization of lie groups and Lie algebras
    • Woronowicz, S.L.: Compact matrix pseudo groups. Commun. Math. Phys. 111, 613 (1987); Faddeev, L.D., Reshetikhin, N.Yu. and Takhtajan, L.A.: Quantization of Lie groups and Lie algebras. Leningrad Math. J. 1, 193 (1990)
    • (1990) Leningrad Math. J. , vol.1 , pp. 193
    • Faddeev, L.D.1    Reshetikhin, N.Yu.2    Takhtajan, L.A.3
  • 28
    • 0003959905 scopus 로고
    • Universite de Montreal, Centre de Recherches Mathematiques, Montreal, PQ
    • Manin, Yu.I.: Quantum Groups and Noncommutative Geometry. Universite de Montreal, Centre de Recherches Mathematiques, Montreal, PQ (1988); Woronowicz, S.L.: Differential calculus on compact matrix pseudo groups (quantum groups). Commun. Math. Phys. 122, 125 (1989); Chu, C.S.,Ho, P.M. and Zumino, B.: Some complex quantum manifolds and their geometry. Preprint
    • (1988) Quantum Groups and Noncommutative Geometry
    • Manin, Yu.I.1
  • 29
    • 1542798257 scopus 로고
    • Differential calculus on compact matrix pseudo groups (quantum groups)
    • Manin, Yu.I.: Quantum Groups and Noncommutative Geometry. Universite de Montreal, Centre de Recherches Mathematiques, Montreal, PQ (1988); Woronowicz, S.L.: Differential calculus on compact matrix pseudo groups (quantum groups). Commun. Math. Phys. 122, 125 (1989); Chu, C.S.,Ho, P.M. and Zumino, B.: Some complex quantum manifolds and their geometry. Preprint
    • (1989) Commun. Math. Phys. , vol.122 , pp. 125
    • Woronowicz, S.L.1
  • 30
    • 0009240614 scopus 로고    scopus 로고
    • Preprint
    • Manin, Yu.I.: Quantum Groups and Noncommutative Geometry. Universite de Montreal, Centre de Recherches Mathematiques, Montreal, PQ (1988); Woronowicz, S.L.: Differential calculus on compact matrix pseudo groups (quantum groups). Commun. Math. Phys. 122, 125 (1989); Chu, C.S.,Ho, P.M. and Zumino, B.: Some complex quantum manifolds and their geometry. Preprint
    • Some Complex Quantum Manifolds and their Geometry
    • Chu, C.S.1    Ho, P.M.2    Zumino, B.3
  • 32
    • 0011018195 scopus 로고
    • Classification of all star irreps of gl(m | n)
    • Gould, M.D. and Zhang, R.B.: Classification of all star irreps of gl(m | n). J. Math. Phys., 31, 2552-2559 (1990)
    • (1990) J. Math. Phys. , vol.31 , pp. 2552-2559
    • Gould, M.D.1    Zhang, R.B.2
  • 34
  • 35
    • 0002119476 scopus 로고
    • Tannaha-Krein duality for compact matrix pseudo groups
    • Woronowicz, S.L.: Tannaha-Krein duality for compact matrix pseudo groups. Inv. Math., 93, 35 (1988)
    • (1988) Inv. Math. , vol.93 , pp. 35
    • Woronowicz, S.L.1
  • 39
    • 0001968061 scopus 로고
    • Borel-Weil-Bott theory for classical Lie supergroups
    • Moscow: VINITI
    • Penkov, I.B.. Borel-Weil-Bott Theory for Classical Lie Supergroups. Sovr. Probl. Math. 32, Moscow: VINITI, 1988 pp. 71-124
    • (1988) Sovr. Probl. Math. , vol.32 , pp. 71-124
    • Penkov, I.B.1
  • 40
    • 0000116241 scopus 로고
    • Cohomology of G/P for classical complex Lie groups of G and characters of some typical G-modules
    • Penkov, I.B. and Serganova, V. Cohomology of G/P for Classical Complex Lie Groups of G and Characters of Some Typical G-Modules. Annales de L'institut Fourier, 39 , 846-873 (1989)
    • (1989) Annales de L'institut Fourier , vol.39 , pp. 846-873
    • Penkov, I.B.1    Serganova, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.