### 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 |
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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

Kessar, R., & Valero-Elizondo, L. (2004). Stable partitions and Alperin's weight conjecture for the symmetric groups in characteristic two.

*Boletin Sociedad Matematica Mexicana*,*10*(1), 53-62.