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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cycle indices for finite orthogonal groups of even characteristic


Authors: Jason Fulman, Jan Saxl and Pham Huu Tiep
Journal: Trans. Amer. Math. Soc. 364 (2012), 2539-2566
MSC (2010): Primary 20G40; Secondary 20C33, 05E15
Published electronically: January 6, 2012
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Abstract: We develop cycle index generating functions for orthogonal groups in even characteristic and give some enumerative applications. A key step is the determination of the values of the complex linear-Weil characters of the finite symplectic group, and their induction to the general linear group, at unipotent elements. We also define and study several natural probability measures on integer partitions.


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Additional Information

Jason Fulman
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
Email: fulman@usc.edu

Jan Saxl
Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, United Kingdom
Email: J.Saxl@dpmms.cam.ac.uk

Pham Huu Tiep
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721-0089
Email: tiep@math.arizona.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05406-7
PII: S 0002-9947(2012)05406-7
Keywords: Random matrix, cycle index, Weil representation, random partition
Received by editor(s): April 15, 2010
Received by editor(s) in revised form: June 21, 2010
Published electronically: January 6, 2012
Additional Notes: The first author was partially supported by NSF grant DMS-0802082 and NSA grant H98230-08-1-0133
The third author was partially supported by NSF grant DMS-0901241.
The authors are grateful to Martin Liebeck for kindly sending them the preprint [26] which plays an important role in the current paper.
Dedicated: Dedicated to Peter M. Neumann on the occasion of his seventieth birthday
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.