Year: 2025
Type: article
Abstract: This paper is devoted to investigating the center of two-parameter quantum groups U r , s ( 𝔤 ) {U_{r,s}(\mathfrak{g})} via establishing the Harish-Chandra homomorphism. Based on the Rosso form and the representation theory of weight modules, we prove that when the rank 𝔤 {\mathfrak{g}} is even, the Harish-Chandra homomorphism is an isomorphism, and in particular, the center of the quantum group U ˘ r , s ( 𝔤 ) {\breve{U}_{r,s}(\mathfrak{g})} of the weight lattice type is a polynomial algebra 𝕂 [ z ϖ 1 , … , z ϖ n ] {\mathbb{K}[z_{\varpi_{1}},\dots,z_{\varpi_{n}}]} , where canonical central elements z λ {z_{\lambda}} ( λ ∈ Λ + {\lambda\in\Lambda^{+}} ) are turned out to be uniformly expressed. For the rank 𝔤 {\mathfrak{g}} to be odd, we figure out a new invertible extra central generator z * {z_{*}} , which does not survive in U q ( 𝔤 ) {U_{q}(\mathfrak{g})} , then the center of U
Source: Forum Mathematicum
Authors: Naihong Hu, Hengyi Wang
Institution: East China Normal University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408919850