### Abstract

Original language | English |
---|---|

Pages (from-to) | 135-155 |

Number of pages | 22 |

Journal | Journal of Algebra |

Volume | 233 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2000 |

Externally published | Yes |

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### Cite this

*Journal of Algebra*,

*233*(1), 135-155. https://doi.org/10.1006/jabr.2000.8431

}

*Journal of Algebra*, vol. 233, no. 1, pp. 135-155. https://doi.org/10.1006/jabr.2000.8431

**Conjugacy classes in maximal parabolic subgroups of the general linear group.** / Murray, Scott.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Conjugacy classes in maximal parabolic subgroups of the general linear group

AU - Murray, Scott

PY - 2000

Y1 - 2000

N2 - 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 GLn(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

AB - 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 GLn(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

U2 - 10.1006/jabr.2000.8431

DO - 10.1006/jabr.2000.8431

M3 - Article

VL - 233

SP - 135

EP - 155

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -