Supercharacters and superclasses for algebra groups

Authors:
Persi Diaconis and I. M. Isaacs

Journal:
Trans. Amer. Math. Soc. **360** (2008), 2359-2392

MSC (2000):
Primary 20C15, 20D15

DOI:
https://doi.org/10.1090/S0002-9947-07-04365-6

Published electronically:
November 20, 2007

MathSciNet review:
2373317

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Abstract | References | Similar Articles | Additional Information

Abstract: We study certain sums of irreducible characters and compatible unions of conjugacy classes in finite algebra groups. These groups generalize the unimodular upper triangular groups over a finite field, and the supercharacter theory we develop extends results of Carlos André and Ning Yan that were originally proved in the upper triangular case. This theory sometimes allows explicit computations in situations where it would be impractical to work with the full character table. We discuss connections with the Kirillov orbit method and with Gelfand pairs, and we give conditions for a supercharacter or a superclass to be an ordinary irreducible character or conjugacy class, respectively. We also show that products of supercharacters are positive integer combinations of supercharacters.

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Additional Information

**Persi Diaconis**

Affiliation:
Department of Mathematics, Stanford University, 450 Serra Mall Bldg. 380, Stanford, California 94305

Email:
diaconis@math.stanford.edu

**I. M. Isaacs**

Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Dr., Madison, Wisconsin 53706

Email:
isaacs@math.wisc.edu

DOI:
https://doi.org/10.1090/S0002-9947-07-04365-6

Received by editor(s):
December 30, 2005

Published electronically:
November 20, 2007

Article copyright:
© Copyright 2007
American Mathematical Society

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