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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Supercharacters and superclasses for algebra groups
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by Persi Diaconis and I. M. Isaacs PDF
Trans. Amer. Math. Soc. 360 (2008), 2359-2392 Request permission

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
  • MR Author ID: 57595
  • 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
  • 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