Asymptotics of Plancherel measures for $GL(n,q)$

A. Dudko

Published 2008-06-08, updated 2008-06-11Version 2

We introduce the Plancherel measure on the set of partition collections, which parameterize irreducible representations of order n general linear group over a finite field. We prove that as n goes to infinity, the random partitions from the random collections converge in finite dimencional distribution to independent random variables. We give explicit formulas for the corresponding limit distributions.