Cycle indices for finite orthogonal groups of even characteristic

Fulman, Jason; Saxl, Jan; Tiep, Pham

doi:10.1090/S0002-9947-2012-05406-7

Cycle indices for finite orthogonal groups of even characteristic
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by Jason Fulman, Jan Saxl and Pham Huu Tiep PDF

Trans. Amer. Math. Soc. 364 (2012), 2539-2566 Request permission

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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