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

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

2009-01-06

arxiv.org/abs/0901.0667v2

Mathematics

Group Theory

8 pages; to appear in Pacific Journal of Mathematics

Scientific paper

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 $\FF_q^n$
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.

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