Conjugacy classes in maximal parabolic subgroups of general linear groups
| dc.creator | Murray, Scott H. | |
| dc.date | 2000-01-06 | |
| dc.date.accessioned | 2026-07-07T04:33:13Z | |
| dc.date.available | 2026-07-07T04:33:13Z | |
| dc.description | 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. | |
| dc.description | 23 pages, 6 figures. See also http://zaphod.uchicago.edu/~murray/research/index.html . Submitted to Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0001031 | |
| dc.identifier | http://arxiv.org/abs/math/0001031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58494 | |
| dc.subject | Group Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 20C | |
| dc.title | Conjugacy classes in maximal parabolic subgroups of general linear groups | |
| dc.type | text |