A generalized Harish-Chandra isomorphism

TL;DR

This paper extends the Harish-Chandra isomorphism to the tensor product of the universal enveloping algebra of a complex reductive Lie algebra with any locally finite module, broadening its applicability.

Contribution

It generalizes the classical Harish-Chandra isomorphism to a wider class of modules and tensor products, providing new insights into invariants in universal enveloping algebras.

Findings

Extended Harish-Chandra isomorphism to tensor products with locally finite modules

Provided a new description of g-invariants in U(g) tensor V

Broadened the scope of classical invariant theory in Lie algebra representations

Abstract

For any complex reductive Lie algebra g and any locally finite g-module V, we extend to the tensor product of U(g) with V the Harish-Chandra description of g-invariants in the universal enveloping algebra U(g).