Representations of two-parameter quantum orthogonal and symplectic groups
Representations of two-parameter quantum orthogonal and symplectic groups
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发表时间：
2005-10
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通讯作者：
N. Bergeron;Yung Gao;N. Hu
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作者：
N. Bergeron;Yung Gao;N. Hu
我们研究有限维表示两参数量子理论正交和辛组,我们发现(使用BGH)假设rs−1不是一个根的团结和扩展(BW1 BW2)获得一些结果类型类型B, C和D我们构建相应的R-matrices和量子卡西米尔运营商,我们证明完整的可约性定理也适用于有限维重量模块类型的类别B, C, D。
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.