On the conjugation action for quantum general linear groups

TL;DR

This paper investigates the conjugation action of quantum general linear groups over arbitrary fields, extending classical results to the quantum setting and providing new algebraic insights.

Contribution

It introduces analogues of classical results for the conjugation action in the context of quantum groups, specifically for the coordinate algebra of quantum GL(n).

Findings

Extended Kostant and Richardson results to quantum groups

Analyzed conjugation actions over arbitrary fields

Provided algebraic structures for quantum GL(n)

Abstract

We consider the conjugation action of a quantum group over an arbitrary field. In particular we consider the coordinate algebra of a quantised general linear group G(n), at an arbitrary nonzero parameter q, and give analogues of results of Kostant and Richardson