Young module multiplicities and classifying the indecomposable Young permutation modules

2012/03/28 by Christopher C. Gill, Gill, Christopher C.
Computer Science · Mathematics · #20C30 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:20C30

paper · pdf · doi:10.48550/arxiv.1203.6370

22 pages

openalex publication_date 2012/03/28 · arxiv created 2015/10/05 · arxiv updated 2015/10/07 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We study the multiplicities of Young modules as direct summands of permutation modules on cosets of Young subgroups. Such multiplicities have become known as the p-Kostka numbers. We classify the indecomposable Young permutation modules, and, applying the Brauer construction for p-permutation modules, we give some new reductions for p-Kostka numbers. In particular we prove that p-Kostka numbers are preserved under multiplying partitions by p, and strengthen a known reduction given by Henke, corresponding to adding multiples of a p-power to the first row of a partition.

Related

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• On signed p-Kostka matrices
• Endomorphism rings of permutation modules over maximal Young subgroups
• On the Brauer constructions and generic Jordan types of Young modules
• On the symmetric and exterior powers of Young permutation modules