Geometry of quantum homogeneous supervector bundles and representation theory of quantum general linear supergroup

被引:0
|
作者
Zhang, RB [1 ]
机构
[1] Univ Adelaide, Dept Pure Math, Adelaide, SA 5005, Australia
关键词
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The quantum general linear supergroup GL(q)(m\n) is defined and its structure is studied systematically. Quantum homogeneous supervector bundles are introduced following Connes' theory, and applied to develop the representation theory of GL(q)(m\n). Quantum Frobenius reciprocity is proven, and a Borel-Weil theorem is established for the covariant and contravariant tensor irreps.
引用
收藏
页码:37 / 39
页数:3
相关论文
共 50 条
  • [41] Quantum control and representation theory
    Ibort, A.
    Perez-Pardo, J. M.
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (20)
  • [42] Representation of Quantum Field Theory by Elementary Quantum Information
    Kober, Martin
    INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2012, 51 (08) : 2476 - 2487
  • [43] Representation of Quantum Field Theory by Elementary Quantum Information
    Martin Kober
    International Journal of Theoretical Physics, 2012, 51 : 2476 - 2487
  • [44] On quantum general linear groups
    Gerritzen, L
    Holtkamp, R
    INDAGATIONES MATHEMATICAE-NEW SERIES, 1997, 8 (01): : 43 - 54
  • [45] FIBER-BUNDLES AND QUANTUM-THEORY
    BERNSTEIN, HJ
    PHILLIPS, AV
    USPEKHI FIZICHESKIKH NAUK, 1982, 136 (04): : 665 - 692
  • [46] DIFFERENTIAL GEOMETRY ON LINEAR QUANTUM GROUPS
    SCHUPP, P
    WATTS, P
    ZUMINO, B
    LETTERS IN MATHEMATICAL PHYSICS, 1992, 25 (02) : 139 - 147
  • [47] FIBER-BUNDLES AND QUANTUM-THEORY
    BERNSTEIN, HJ
    PHILLIPS, AV
    SCIENTIFIC AMERICAN, 1981, 245 (01) : 123 - &
  • [48] QUANTUM LINEAR GEOMETRY AND PARALLEL TRANSFER
    Fock, V.
    Iwanenko, D.
    UKRAINIAN JOURNAL OF PHYSICS, 2008, 53 : 11 - 13
  • [49] Remarks on the GNS Representation and the Geometry of Quantum States
    Chruscinski, Dariusz
    Marmo, Giuseppe
    OPEN SYSTEMS & INFORMATION DYNAMICS, 2009, 16 (2-3): : 157 - 177
  • [50] LINEAR QUANTUM ENSKOG EQUATION .1. HOMOGENEOUS QUANTUM FLUIDS
    LOSS, D
    JOURNAL OF STATISTICAL PHYSICS, 1990, 59 (3-4) : 691 - 723