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A Probabilistic Approach Toward Conjugacy Classes in the Finite General Linear and Unitary Groups

โœ Scribed by Jason Fulman

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
205 KB
Volume
212
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

The conjugacy classes of the finite general linear and unitary groups are used to define probability measures on the set of all partitions of all natural numbers. Probabilistic algorithms for growing random partitions according to these measures are obtained. These algorithms are applied to prove group theoretic results which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's count of unipotent elements, Rudvalis' and Shinoda's work on the fixed space of a random matrix, and Lusztig's count of nilpotent matrices of a given rank. Generalizations of these algorithms based on Macdonald's symmetric functions are given.

๐Ÿ“œ SIMILAR VOLUMES

A Probabilistic Approach to Conjugacy Cl
A Probabilistic Approach to Conjugacy Classes in the Finite Symplectic and Orthogonal Groups
โœ Jason Fulman ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 135 KB

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