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Supercharacters and pattern subgroups in the upper triangular groups (1008.2269v2)
Published 13 Aug 2010 in math.RT and math.GR
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 $k<n.$