Characters of 2-layered Heisenberg groups

Abstract

We give a classification of irreducible representations of generalized Heisenberg groups which is the pattern group associated to the closed set In light of the conjectures of Higman, Lehrer and Isaacs for unitriangular groups, this result shows that the number of irreducible characters of with a fixed degree is a polynomial in q−1 with non-negative integer coefficients.