On signed Young permutation modules and signed p-Kostka numbers

Eugenio Giannelli, Kay Jin Lim, William O'Donovan, Mark Wildon

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Abstract

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.
Original languageEnglish
Pages (from-to)637–679
Number of pages43
JournalJournal of Group Theory
Volume20
Issue number4
Early online date25 Feb 2017
DOIs
Publication statusPublished - 1 Jul 2017

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