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Conjugacy classes in maximal parabolic subgroups of general linear groups | | Scott H. Murray
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6 Dec 1999 | | Subject: | Group Theory; Representation Theory MSC-class: 20C | math.GR math.RT | | Affiliation: | University of Chicago | | Abstract: | 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. | | Source: | arXiv, math.GR/0001031 | | Services: | Forum | Review | PDF | Favorites | |
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