A generalized Steinberg section and branching rules for quantum groups at roots of 1

TL;DR

This paper generalizes the Steinberg section for semisimple groups and applies it to construct a Gelfand-Zetlin basis for quantum GL(n) at roots of unity, advancing representation theory of quantum groups.

Contribution

It introduces a generalized Steinberg section for semisimple groups and applies it to quantum groups at roots of unity, providing new tools for representation theory.

Findings

Construction of a generalized Steinberg section for semisimple groups.

Development of a Gelfand-Zetlin basis for quantum GL(n) at roots of unity.

Applications to branching rules and representation analysis.

Abstract

In this paper we construct a generalization of the classical Steinberg section for the quotient map of a semisimple group with respect to the conjugation action. We then give various applications of our construction including the construction of a sort of Gelfand Zetlin basis for a generic irreducible representation of quantum GL(n) at odd roots of unity.