Structure and Representations of the Quantum General Linear Supergroup
Structure and Representations of the Quantum General Linear Supergroup
复制标题
DOI：
10.1007/s002200050401
复制
发表时间：
1996-11
影响因子：
2.4
通讯作者：
R. Zhang
中科院分区：
文献类型：
--
作者：
R. Zhang
通过研究量子一般线性超群Gq的代表函数的Hopf超代数Gq，系统地研究了GLq(m|n)的结构和表示，将Gq分解为Gq，并为每个因子构造了Peter-Weyl基.发展了量子超群的抛物线归纳法。讨论了诱导表示的基本几何，得到了Frobenius互易的模拟。证明了不可约协变张量表示和逆变张量表示的量子Borel-Weil定理，并给出了量子射影超空间上不可约张量表示关于量子超向量丛截面的显式实现.
The structure and representations of the quantum general linear supergroupGLq(m|n) are studied systematically by investigating the Hopf superalgebraGqof its representative functions.Gqis factorized into, and a Peter–Weyl basis is constructed for each factor. Parabolic induction for the quantum supergroup is developed. The underlying geometry of induced representations is discussed, and an analog of Frobenius reciprocity is obtained. A quantum Borel–Weil theorem is proven for the irreducible covariant and contravariant tensorial representations, and explicit realizations are given for classes of irredducible tensorial representatins in terms of sections of quantum super vector bundles over quantum projective superspaces.