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.

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• On the U-module Structure of the Unipotent Specht Modules of Finite General Linear Groups
• Counting irreducible representations of large degree of the upper triangular groups