### Abstract

Alperin's weight conjecture for the symmetric groups has been proved using an enumeration of the weights and the simple modules (see [2]), but so far there is no explicit way to associate weights with simple modules. Based on data obtained using an algorithm for finding weights for small symmetric groups in characteristic two (see [16]), we put forward a combinatorial conjecture which, if true, would provide explicit bijections between weights and irreducible modules for the symmetric groups in characteristic two. We prove some results towards the proof of this combinatorial conjecture.

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

Pages (from-to) | 53-62 |

Number of pages | 9 |

Journal | Boletin Sociedad Matematica Mexicana |

Volume | 10 |

Issue number | 1 |

Publication status | Published - 2004 |

### Keywords

- group representation
- Alperin's conjecture
- weight
- Brauer quotient
- symmetric group
- partition
- GENERAL LINEAR-GROUPS
- HECKE ALGEBRAS
- 2-WEIGHTS

### Cite this

*Boletin Sociedad Matematica Mexicana*,

*10*(1), 53-62.

**Stable partitions and Alperin's weight conjecture for the symmetric groups in characteristic two.** / Kessar, Radha; Valero-Elizondo, L.

Research output: Contribution to journal › Article

*Boletin Sociedad Matematica Mexicana*, vol. 10, no. 1, pp. 53-62.

}

TY - JOUR

T1 - Stable partitions and Alperin's weight conjecture for the symmetric groups in characteristic two

AU - Kessar, Radha

AU - Valero-Elizondo, L.

PY - 2004

Y1 - 2004

N2 - Alperin's weight conjecture for the symmetric groups has been proved using an enumeration of the weights and the simple modules (see [2]), but so far there is no explicit way to associate weights with simple modules. Based on data obtained using an algorithm for finding weights for small symmetric groups in characteristic two (see [16]), we put forward a combinatorial conjecture which, if true, would provide explicit bijections between weights and irreducible modules for the symmetric groups in characteristic two. We prove some results towards the proof of this combinatorial conjecture.

AB - Alperin's weight conjecture for the symmetric groups has been proved using an enumeration of the weights and the simple modules (see [2]), but so far there is no explicit way to associate weights with simple modules. Based on data obtained using an algorithm for finding weights for small symmetric groups in characteristic two (see [16]), we put forward a combinatorial conjecture which, if true, would provide explicit bijections between weights and irreducible modules for the symmetric groups in characteristic two. We prove some results towards the proof of this combinatorial conjecture.

KW - group representation

KW - Alperin's conjecture

KW - weight

KW - Brauer quotient

KW - symmetric group

KW - partition

KW - GENERAL LINEAR-GROUPS

KW - HECKE ALGEBRAS

KW - 2-WEIGHTS

M3 - Article

VL - 10

SP - 53

EP - 62

JO - Boletin Sociedad Matematica Mexicana

JF - Boletin Sociedad Matematica Mexicana

SN - 1405-213X

IS - 1

ER -