Supercharacter formulas for pattern groups

Diaconis, Persi; Thiem, Nathaniel

doi:10.1090/S0002-9947-09-04521-8

Supercharacter formulas for pattern groups
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by Persi Diaconis and Nathaniel Thiem PDF

Trans. Amer. Math. Soc. 361 (2009), 3501-3533 Request permission

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 $U_n(\mathbb {F}_q)$. 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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