On signed Young permutation modules and signed p-Kostka numbers
Lim, Kay Jin
Date of Issue2017
School of Physical and Mathematical Sciences
We prove the existence and main properties of signed Young modules for the symmetric group, using only basic facts about symmetric group representations and the Broué correspondence. We then prove new reduction theorems for the signed p-Kostka numbers, defined to be the multiplicities of signed Young modules as direct summands of signed Young permutation modules. We end by classifying the indecomposable signed Young permutation modules and determining their endomorphism algebras.
Journal of Group Theory
© 2017 Walter de Gruyter GmbH. This paper was published in Journal of Group Theory and is made available as an electronic reprint (preprint) with permission of Walter de Gruyter GmbH. The published version is available at: [http://dx.doi.org/10.1515/jgth-2017-0007]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.