A Probabilistic Approach toward Conjugacy Classes in the Finite General Linear and Unitary Groups
نویسنده
چکیده
The conjugacy classes of the nite general linear and unitary groups are used to de ne 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 Shindoda's work on the xed 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.
منابع مشابه
On the Regular Power Graph on the Conjugacy Classes of Finite Groups
emph{The (undirected) power graph on the conjugacy classes} $mathcal{P_C}(G)$ of a group $G$ is a simple graph in which the vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent in $mathcal{P_C}(G)$ if one is a subset of a power of the other. In this paper, we describe groups whose associated graphs are $k$-regular for $k=5,6$.
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متن کاملA Probabilistic Approach toward the Finite General Linear and Unitary Groups
Abstract Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups 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 Shindoda’s work on the fixed space of a random matrix, and Lusztig’s work on counting nilpotent matrices of ...
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تاریخ انتشار 2007