On the Harish-Chandra Homomorphism for Quantum Superalgebras

Abstract

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

arXiv comment35 pages, comments are welcome!

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Cited by in corpus (3)

• The quantum isomeric supercategory
• Quantum Supergroup $U_{r,s}(osp(1,2))$, Scasimir Operators, and Dickson polynomials
• Harish-Chandra Theorem for Two-parameter Quantum Groups