A quantum analogue of Kostant's theorem for the general linear group

TL;DR

This paper establishes a quantum analogue of Kostant's theorem for the general linear group, extending classical representation theory results into the quantum setting and applying them to reflection equation algebras.

Contribution

It introduces a novel quantum version of Kostant's theorem specifically for the general linear group, expanding the understanding of quantum invariants in representation theory.

Findings

Proves a quantum analogue of Kostant's theorem for GL(n)

Derives results for reflection equation algebras

Extends classical invariant theory into quantum groups

Abstract

A fundamental result in representation theory is Kostant's theorem which describes the algebra of polynomials on a reductive Lie algebra as a module over its invariants. We prove a quantum analogue of this theorem for the general linear group, and from this deduce the analogous result for reflection equation algebras.