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

2013/11/28 by Richard Dipper, Dipper, Richard, Qiong Guo +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1311.7294

arxiv created 2013/12/12 · arxiv updated 2013/12/13

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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