### Abstract

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

Pages (from-to) | 4132-4162 |

Number of pages | 31 |

Journal | Communications in Algebra |

Volume | 36 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2 Dec 2008 |

### Fingerprint

### Keywords

- block theory
- finite general linear group
- generalized blocks
- Nakayama conjecture
- representation theory
- unipotent characters

### Cite this

**Generalized blocks of unipotent characters in the finite general linear group.** / Gramain, Jean-Baptiste.

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 36, no. 11, pp. 4132-4162. https://doi.org/10.1080/00927870802175055

}

TY - JOUR

T1 - Generalized blocks of unipotent characters in the finite general linear group

AU - Gramain, Jean-Baptiste

PY - 2008/12/2

Y1 - 2008/12/2

N2 - In an article of 2003, Külshammer, Olsson, and Robinson defined l-blocks for the symmetric groups, where l > 1 is an arbitrary integer, and proved that they satisfy an analogue of the Nakayama Conjecture. Inspired by this work and the definitions of generalized blocks and sections given by the authors, we give in this article a definition of d-sections in the finite general linear group, and construct d-blocks of unipotent characters, where d = 1 is an arbitrary integer. We prove that they satisfy one direction of an analogue of the Nakayama Conjecture, and, in some cases, prove the other direction. We also prove that they satisfy an analogue of Brauer's Second Main Theorem.

AB - In an article of 2003, Külshammer, Olsson, and Robinson defined l-blocks for the symmetric groups, where l > 1 is an arbitrary integer, and proved that they satisfy an analogue of the Nakayama Conjecture. Inspired by this work and the definitions of generalized blocks and sections given by the authors, we give in this article a definition of d-sections in the finite general linear group, and construct d-blocks of unipotent characters, where d = 1 is an arbitrary integer. We prove that they satisfy one direction of an analogue of the Nakayama Conjecture, and, in some cases, prove the other direction. We also prove that they satisfy an analogue of Brauer's Second Main Theorem.

KW - block theory

KW - finite general linear group

KW - generalized blocks

KW - Nakayama conjecture

KW - representation theory

KW - unipotent characters

U2 - 10.1080/00927870802175055

DO - 10.1080/00927870802175055

M3 - Article

VL - 36

SP - 4132

EP - 4162

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 11

ER -