Parabolic conjugacy in general linear groups
arXiv:math/0611780
Abstract
Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL(n,q). We show that the number of P(q)-conjugacy classes in GL(n,q) is, as a function of q, a polynomial in q with integer coefficients. This answers a question of J. Alperin.
12 pages; to appear in Journal of Algebraic Combinatorics