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

Fulman, Jason

doi:10.1090/S0002-9939-99-05292-2

The Rogers-Ramanujan identities, the finite general linear groups, and the Hall-Littlewood polynomials
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Proc. Amer. Math. Soc. 128 (2000), 17-25 Request permission

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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