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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- Persi Diaconis
- Affiliation: Department of Mathematics, Stanford University, 450 Serra Mall Bldg. 380, Stanford, California 94305
- MR Author ID: 57595
- Email: email@example.com
- I. M. Isaacs
- Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Dr., Madison, Wisconsin 53706
- Email: firstname.lastname@example.org
- Received by editor(s): December 30, 2005
- Published electronically: November 20, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- 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
- MathSciNet review: 2373317