Representations of Two-parameter Quantum Orthogonal and Symplectic Groups

Nantel Bergeron; Yun Gao; Naihong Hu

Representations of Two-parameter Quantum Orthogonal and Symplectic Groups

量子代数 2010-03-31 v1 表示论

作者: Nantel Bergeron , Yun Gao , Naihong Hu

摘要

We investigate the finite-dimensional representation theory of two-parameter quantum orthogonal and symplectic groups that we found in [BGH] under the assumption that $rs^{-1}$ is not a root of unity and extend some results [BW1, BW2] obtained for type $A$ to types $B$ , $C$ and $D$ . We construct the corresponding $R$ -matrices and the quantum Casimir operators, by which we prove that the complete reducibility Theorem also holds for the categories of finite-dimensional weight modules for types $B$ , $C$ , $D$ .

关键词

representation theory representation theory of groups group representations

引用

@article{arxiv.math/0510124,
  title  = {Representations of Two-parameter Quantum Orthogonal and Symplectic Groups},
  author = {Nantel Bergeron and Yun Gao and Naihong Hu},
  journal= {arXiv preprint arXiv:math/0510124},
  year   = {2010}
}

Representations of Two-parameter Quantum Orthogonal and Symplectic Groups

摘要

关键词

引用

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