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

2009/01/06 by Simon M. Goodwin, Gerhard Roehrle, Goodwin, Simon M. +1
Mathematics · #20G40 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0901.0667

openalex publication_date 2009/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \FF_qⁿ of length at most 5, and let U = O_p(P). In this note 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.

Related

• Parabolic conjugacy in general linear groups
• Conjugacy classes in parabolic subgroups of general linear groups
• Conjugacy classes in maximal parabolic subgroups of general linear groups
• Polynomial properties of unipotent radicals of parabolic subgroups in classical groups
• On conjugacy of unipotent elements in finite groups of Lie type