Explicit generators of the centre of the quantum group

Abstract

For a slightly generalised version of the Jimbo quantum group associated with any finite dimensional simple Lie algebra $\mathfrak{g}$, 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 $\mathfrak{g}$, 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.