On the Harish-Chandra Homomorphism for Quantum Superalgebras

作者：Luo, Yang^*; Wang, Yongjie; Ye, Yu

来源：Communications in Mathematical Physics, 2022.

DOI：10.1007/s00220-022-04394-x

• UNIVERSAL-R-MATRICES
• DIMENSIONAL IRREDUCIBLE REPRESENTATIONS
• GENERALIZED GELFAND INVARIANTS
• LIE-SUPERALGEBRAS
• DRINFELD REALIZATION
• AFFINE ALGEBRA
• ISOMORPHISMS
• THEOREM
• FORM

In this paper, we introduce the Harish-Chandra homomorphism for the quantum superalgebra U-q(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 U-q(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 U-q(g). As a byproduct, we obtain a basis of the center of U-q(g) with the aid of quasi-R-matrix.

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