Trace of powers of representations of finite quantum groups

Abstract

In this paper we study (asymptotic) properties of the $*$-distribution of irreducible characters of finite quantum groups. We proceed in two steps, first examining the representation theory to determine irreducible representations and their powers, then we study the $*$-distribution of their trace with respect to the Haar measure. For the Sekine family we look at the asymptotic distribution (as the dimension of the algebra goes to infinity).