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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Rogers-Ramanujan identities,
the finite general linear groups,
and the Hall-Littlewood polynomials


Author: Jason Fulman
Journal: Proc. Amer. Math. Soc. 128 (2000), 17-25
MSC (1991): Primary 20P05, 05E05
Published electronically: June 30, 1999
MathSciNet review: 1657747
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Abstract: We connect Gordon's generalization of the Rogers-Ramanujan identities with the Hall-Littlewood polynomials and with generating functions which arise in a probabilistic setting in the finite general linear groups. This yields a Rogers-Ramanujan type product formula for the $n \rightarrow \infty$ probability that an element of $GL(n,q)$ or $Mat(n,q)$ is semisimple.


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Additional Information

Jason Fulman
Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551
Email: Fulman@Dartmouth.Edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05292-2
Received by editor(s): March 6, 1998
Published electronically: June 30, 1999
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society