Character values and decomposition matrices of symmetric groups

JOURNAL OF ALGEBRA

卷:319

Article

Wildon, Mark

关键词: symmetric group;    decomposition matrix;    Specht module;    alternating group;    centre of group algebra;   

DOI  :  10.1016/j.jalgebra.2007.11.017

来源: Elsevier

【 摘 要 】

The relationships between the values taken by ordinary characters of symmetric groups are exploited to prove two theorems in the modular representation theory of the symmetric group. 1. The decomposition matrices of symmetric groups in odd characteristic have distinct rows. In characteristic 2 the rows of a decomposition matrix labelled by the different partitions lambda and mu are equal if and only if lambda and mu are conjugate. An analogous result is proved for Hecke algebras. 2. A Specht module for the symmetric group S-n, defined over an algebraically closed field of odd characteristic, is decomposable on restriction to the alternating group A(n) if and only if it is simple, and the labelling partition is self-conjugate. This result is generalised to an arbitrary field of odd characteristic. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free