Irreducible constituents of minimal degree in supercharacters of the finite unitriangular groups

Abstract

Let q be a prime power and U the group of lower unitriangular matrices of order n for some natural number n. We give a lower bound for the degrees of irreducible constituents of André–Yan supercharacters and classify the supercharacters having constituents whose degree assume this lower bound. Moreover we show that the number of distinct irreducible characters of U meeting this condition is a polynomial in (q−1) with nonnegative integral coefficients and exhibit monomial sources for those.