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Quantum Algorithms

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

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Authors: Kaixiang CHEN, Naihong HU, Hengyi WANG

Year

2026

Paper ID

77105

Status

Peer-reviewed

Abstract Read

~2 min

Abstract Words

100

Citations

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 \(U⁰_flat\)^W is isomorphic to a polynomial algebra or a quotient algebra of a polynomial algebra. The same result holds for the \(U⁰_flat\)^W of the two-parameter quantum group U_r,s\(mathfrak{g}\).

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This paper is devoted to studying the centre of the multi-parameter quantum group Uq,G(mathfrakg) introduced by Okado and Yamane, where mathfrakg is a complex simple Lie...

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References & Citation Signals

[1] DOI https://doi.org/10.2969/jmsj/96149614 [2] Publisher https://doi.org/10.2969/jmsj/96149614

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