The Harish-Chandra isomorphism for reductive symmetric superpairs

TL;DR

This paper extends the Harish-Chandra isomorphism to strongly reductive symmetric pairs of Lie superalgebras, identifying the image as a specific subalgebra of Weyl invariants, generalizing classical results.

Contribution

It introduces a graded Harish-Chandra homomorphism for symmetric superpairs and characterizes its image explicitly, generalizing prior classical and superalgebra results.

Findings

The image of the homomorphism is a filtered subalgebra of Weyl invariants.

The associated graded of this subalgebra matches Chevalley's restriction map.

The results generalize classical Harish-Chandra and Kac's theorems.

Abstract

We consider symmetric pairs of Lie superalgebras which are strongly reductive and of even type, and introduce a graded Harish-Chandra homomorphism. We prove that its image is a certain explicit filtered subalgebra of the Weyl invariants on a Cartan subspace whose associated graded is the image of Chevalley's restriction map on symmetric invariants. This generalises results of Harish-Chandra and V. Kac, M. Gorelik.