Representations of Two-parameter Quantum Orthogonal and Symplectic Groups

Details Representations of Two-parameter Quantum Orthogonal and Symplectic Groups Representations of Two-parameter Quantum Orthogonal and Symplectic Groups

2005-10-06

arxiv.org/abs/math/0510124v1

AMS/IP Stud. Adv. Math., 39, Amer. Math. Soc., Providence, RI, 2007

Mathematics

Quantum Algebra

Scientific paper

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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