A Probabilistic Approach to Conjugacy Classes in the Finite Symplectic and Orthogonal Groups

Mathematics – Group Theory

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Revised version; to appear in J. Algebra. Same results. We fix a possibly misleading typo, replacing u by u^2 in some normaliz

Scientific paper

Markov chains are used to give a purely probabilistic way of understanding
the conjugacy classes of the finite symplectic and orthogonal groups in odd
characteristic. As a corollary of these methods one obtains a probabilistic
proof of Steinberg's count of unipotent matrices and generalizations of
formulas of Rudvalis and Shinoda.

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