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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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Cross characteristic representations of even characteristic symplectic groups
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by Robert M. Guralnick and Pham Huu Tiep PDF
Trans. Amer. Math. Soc. 356 (2004), 4969-5023 Request permission

Abstract:

We classify the small irreducible representations of $Sp_{2n}(q)$ with $q$ even in odd characteristic. This improves even the known results for complex representations. The smallest representation for this group is much larger than in the case when $q$ is odd. This makes the problem much more difficult.
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Additional Information
  • Robert M. Guralnick
  • Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532
  • MR Author ID: 78455
  • Email: guralnic@math.usc.edu
  • Pham Huu Tiep
  • Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
  • MR Author ID: 230310
  • Email: tiep@math.ufl.edu
  • Received by editor(s): June 5, 2002
  • Received by editor(s) in revised form: July 29, 2003
  • Published electronically: April 27, 2004
  • Additional Notes: Part of this paper was written while the authors were participating in the Symposium “Groups, Geometries, and Combinatorics”, London Mathematical Society, July 16–26, 2001, Durham, England. It is a pleasure to thank the organizers A. A. Ivanov, M. W. Liebeck, and J. Saxl for their generous hospitality and support. The authors are also thankful to the referee for helpful comments on the paper.
    The authors gratefully acknowledge the support of the NSF (grants DMS-9970305, DMS-0140578 and DMS-0070647) and the NSA
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 4969-5023
  • MSC (2000): Primary 20C33, 20G05, 20C20, 20G40
  • DOI: https://doi.org/10.1090/S0002-9947-04-03477-4
  • MathSciNet review: 2084408