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Cross characteristic representations of even characteristic symplectic groups

Author(s): Robert M. Guralnick; Pham Huu Tiep
Journal: Trans. Amer. Math. Soc. 356 (2004), 4969-5023.
MSC (2000): Primary 20C33, 20G05, 20C20, 20G40
Posted: April 27, 2004
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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
Email: guralnic@math.usc.edu

Pham Huu Tiep
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: tiep@math.ufl.edu

DOI: 10.1090/S0002-9947-04-03477-4
PII: S 0002-9947(04)03477-4
Keywords: Finite symplectic group, Weil representation, cross characteristic representation, low dimensional representation
Received by editor(s): June 5, 2002
Received by editor(s) in revised form: July 29, 2003
Posted: 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 of article: Copyright 2004, American Mathematical Society

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