On signed Young permutation modules and signed p-Kostka numbers

On signed Young permutation modules and signed p-Kostka numbers

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 Youn...

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Bibliographic Details
Main Authors: Giannelli, Eugenio, Lim, Kay Jin, O’Donovan, William, Wildon, Mark
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2018
Subjects:
Permutation
Young Modules
DRNTU::Science::Mathematics
Online Access:https://hdl.handle.net/10356/88467
http://hdl.handle.net/10220/45793
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.

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