Work

Harish-Chandra theorem for the multi-parameter quantum groups of Okado–Yamane type

Year: 2026

Type: article

Abstract: This paper is devoted to studying the centre of the multi-parameter quantum group $U_{q,G}(\mathfrak{g})$ introduced by Okado and Yamane, where $\mathfrak{g}$ is a complex simple Lie algebra, and all parameters lie in general position. We mainly establish the Harish-Chandra theorem, proving that the Harish-Chandra homomorphism is an isomorphism; in particular, we determine the centre $Z(U_{q,G}) \cong (U^{0}_{\flat})^{W}$ is isomorphic to a polynomial algebra or a quotient algebra of a polynomial algebra. The same result holds for the $(U^{0}_{\flat})^{W}$ of the two-parameter quantum group $U_{r,s}(\mathfrak{g})$.

Source: Journal of the Mathematical Society of Japan

DOI: 10.2969/jmsj/96149614

Authors: Kaixiang CHEN, Naihong HU, Hengyi WANG

Institution: East China Normal University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Science and Technology Commission of Shanghai Municipality

Awards: G1609915050, G3466989150, G7270659173