Supercharacters and pattern subgroups in the upper triangular groups

Tung Le

Supercharacters and pattern subgroups in the upper triangular groups

Representation Theory 2013-08-06 v2 Group Theory

Authors: Tung Le

Abstract

Let $U_n(q)$ denote the upper triangular group of degree $n$ over the finite field $\F_q$ with $q$ elements. It is known that irreducible constituents of supercharacters partition the set of all irreducible characters $\Irr(U_n(q)).$ In this paper we present a correspondence between supercharacters and pattern subgroups of the form $U_k(q)\cap {}^wU_k(q)$ where $w$ is a monomial matrix in $GL_k(q)$ for some $k<n.$

Keywords

character theory of finite groups character theory finite fields

Cite

@article{arxiv.1008.2269,
  title  = {Supercharacters and pattern subgroups in the upper triangular groups},
  author = {Tung Le},
  journal= {arXiv preprint arXiv:1008.2269},
  year   = {2013}
}

Comments

12 pages

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