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

Author(s): Jason Fulman
Journal: Proc. Amer. Math. Soc. 128 (2000), 17-25.
MSC (1991): Primary 20P05, 05E05
Posted: June 30, 1999
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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: 10.1090/S0002-9939-99-05292-2
PII: S 0002-9939(99)05292-2
Received by editor(s): March 6, 1998
Posted: June 30, 1999
Communicated by: Ronald M. Solomon
Copyright of article: Copyright 1999, American Mathematical Society

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