Conjugacy classes in parabolic subgroups of general linear groups

Details Conjugacy classes in parabolic subgroups of general linear groups Conjugacy classes in parabolic subgroups of general linear groups

2008-01-21

arxiv.org/abs/0801.3178v1

Mathematics

Group Theory

with an appendix by Anton Evseev and George Wellen; 30 pages

Scientific paper

We prove a formula connecting the number of unipotent conjugacy classes in a maximal parabolic subgroup of a finite general linear group with the numbers of unipotent conjugacy classes in various parabolic subgroups in smaller dimensions. We generalise this formula and deduce a number of corollaries; in particular, we express the number of conjugacy classes of unitriangular matrices over a finite field in terms of the numbers of unipotent conjugacy classes in maximal parabolic subgroups over the same field. We show how the numbers of unipotent conjugacy classes in parabolic subgroups of small dimensions may be calculated.

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