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Representations of Two-parameter Quantum Orthogonal and Symplectic Groups

Nantel Bergeron·Yun Gao·Naihong Hu
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Abstract

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 $B$, $C$, $D$.

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Nantel Bergeron, Yun Gao, Naihong Hu. 2005-10-06. Representations of Two-parameter Quantum Orthogonal and Symplectic Groups. https://arxiv.org/abs/math/0510124

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