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

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.