Supercharacter formulas for pattern groups

Authors:
Persi Diaconis and Nathaniel Thiem

Journal:
Trans. Amer. Math. Soc. **361** (2009), 3501-3533

MSC (2000):
Primary 20C99, 05Exx

DOI:
https://doi.org/10.1090/S0002-9947-09-04521-8

Published electronically:
March 4, 2009

MathSciNet review:
2491890

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Abstract | References | Similar Articles | Additional Information

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 . 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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Additional Information

**Persi Diaconis**

Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305-4065

**Nathaniel Thiem**

Affiliation:
Department of Mathematics, Stanford University, 450 Serra Mall, Building 380, Stanford, California 94305-2125

Address at time of publication:
Department of Mathematics, University of Colorado, Campus Box 395, Boulder, Colorado 80309-0395

DOI:
https://doi.org/10.1090/S0002-9947-09-04521-8

Keywords:
Supercharacters,
superclasses,
finite unipotent group,
algebra group,
posets

Received by editor(s):
October 5, 2006

Received by editor(s) in revised form:
March 1, 2007

Published electronically:
March 4, 2009

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.