Trace of powers of representations of finite quantum groups

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).