Counting conjugacy classes in the unipotent radical of parabolic subgroups of GL_n(q)

Simon M. Goodwin and Gerhard Röhrle

Vol. 245 (2010), No. 1, 47–56

DOI: 10.2140/pjm.2010.245.47

Abstract

Let q be a power of a prime p. Let P be a parabolic subgroup of the general linear group GL_n(q) that is the stabilizer of a flag in 𝔽_qⁿ of length at most 5, and let U = O_p(P). We prove that, as a function of q, the number k(U) of conjugacy classes of U is a polynomial in q with integer coefficients.

Keywords

Higman conjecture, parabolic subgroups, unipotent radical

Mathematical Subject Classification 2000

Primary: 20G40

Secondary: 20E45, 20D15

Milestones

Received: 9 January 2009

Accepted: 11 June 2009

Published: 20 January 2010