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Conjugacy Classes in Maximal Parabolic Subgroups of General Linear Groups

✍ Scribed by Scott H. Murray

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
184 KB
Volume
233
Category
Article
ISSN
0021-8693

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✦ Synopsis

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.

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