On the Center of Two-parameter Quantum Groups $U_{r,s}({\mathfrak{so}}_{2n+1})$

Abstract

The paper mainly considers the center of two-parameter quantum groups $U_{r,s}({\mathfrak{so}}_{2n+1})$ via an analogue of the Harish-Chandra homomorphism. In the case when $n$ is odd, the Harish-Chandra homomorphism is not injective in general. When $n$ is even, the Harish-Chandra homomorphism is injective and the center of two-parameter quantum groups $U_{r,s}({\mathfrak{so}}_{2n+1})$ is described, up to isomorphism.

15 pages

References in corpus (5)

• Drinfel'd Doubles and Lusztig's Symmetries of Two-Parameter Quantum Groups
• Two-parameter Quantum Affine Algebra $U_{r,s}(\widehat{{\mathfrak{sl}}_n})$, Drinfel'd Realization and Quantum Affine Lyndon Basis
• Convex PBW-Type Lyndon Bases and Restricted Two-parameter Quantum Groups of Type B
• Notes on two-parameter quantum groups, (II)
• Notes on two-parameter quantum groups, (I)

Cited by in corpus (2)

• Quantum Supergroup $U_{r,s}(osp(1,2))$, Scasimir Operators, and Dickson polynomials
• Harish-Chandra Theorem for Two-parameter Quantum Groups