Explicit generators of the centre of the quantum group

2019/11/18 by Dai, Yanmin · 2 citations
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1912.04021

Abstract

For a slightly generalised version of the Jimbo quantum group associated with any finite dimensional simple Lie algebra \mathfrakg, we show that its centre is a polynomial algebra. We construct a set of algebraically independent central elements, each associated with a fundamental weight of \mathfrakg, and prove that they generate the entire centre of the quantum group. A key ingredient in the proofs of these results is a quantum Harish-Chandra isomorphism for the generalised quantum group, which is proven in some details.

Cited by

• Higher-order Casimir elements and hook partitions for quantum groups of types B, C and D
• Harish-Chandra Theorem for the Multi-Parameter Quantum Groups of Okado-Yamane Type

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