Constructing all irreducible Specht modules in a block of the symmetric group
组合数学
2007-05-23 v1 表示论
摘要
For any prime p, we construct, and simultaneously count, all of the complex Specht modules in a given p-block of the symmetric group which remain irreducible when reduced modulo p. We call the Specht modules with this property p-irreducible modules. Recently Fayers has proven a conjecture of James and Mathas that provides a characterization of the partitions that correspond to the p-irreducible modules. In this paper we present a method for decomposing the partitions corresponding to p-irreducible modules, and we use this decomposition to construct and count all of the partitions corresponding to p-irreducible Specht modules in a given block.
引用
@article{arxiv.math/0605654,
title = {Constructing all irreducible Specht modules in a block of the symmetric group},
author = {James P. Cossey and Matthew Ondrus and C. Ryan Vinroot},
journal= {arXiv preprint arXiv:math/0605654},
year = {2007}
}