On the Harish-Chandra Homomorphism for Quantum Superalgebras

Abstract

In this paper, we introduce the Harish-Chandra homomorphism for the quantum superalgebra Uq(g) associated with a simple basic Lie superalgebra g and give an explicit description of its image. We use it to prove that the center of Uq(g) is isomorphic to a subring of the ring J(g) of exponential super-invariants in the sense of Sergeev and Veselov, establishing a Harish-Chandra type theorem for Uq(g). As a byproduct, we obtain a basis of the center of Uq(g) with the aid of quasi-R-matrix.