Conjugacy classes in maximal parabolic subgroups of general linear groups

JOURNAL OF ALGEBRA

卷:233

Article

Murray, SH

关键词: conjugacy classes;    parabolic subgroup;    general linear group;   

DOI  :  10.1006/jabr.2000.8431

来源: Elsevier

【 摘 要 】

We compute conjugacy classes in maximal parabolic subgroups of the general linear group. This computation proceeds by reducing to a matrix problem. Such problems involve finding normal forms for matrices under a specified set of row and column operations. We solve the relevant matrix problem in small dimensional cases. This gives us all conjugacy classes in maximal parabolic subgroups over a perfect field when one of the two blocks has dimension less than 6. In particular, this includes every maximal parabolic subgroup of GL(n)(k) for n < 12 and k a perfect field. If our field is finite of size q, we also show that the number of conjugacy classes, and so the number of characters, of these groups is a polynomial in q with integral coefficients, (C) 2000 Academic press.

【 授权许可】

Free