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arXiv · 1311.7294

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

Richard Dipper·Qiong Guo
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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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Richard Dipper, Qiong Guo. 2013-12-12. Irreducible constituents of minimal degree in supercharacters of the finite unitriangular groups. https://arxiv.org/abs/1311.7294

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