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Supercharacter formulas for pattern groups

Persi Diaconis·Nathaniel Thiem
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Abstract

C. Andre and N. Yan introduced the idea of a supercharacter theory to give a tractable substitute for character theory in wild groups such as the unipotent uppertriangular group $U_n(F_q)$. In this theory superclasses are certain unions of conjugacy classes, and supercharacters are a set of characters which are constant on superclasses. This paper gives a character formula for a supercharacter evaluated at a superclass for pattern groups and more generally for algebra groups.

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Persi Diaconis, Nathaniel Thiem. 2006-10-04. Supercharacter formulas for pattern groups. https://arxiv.org/abs/math/0610161

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