Young module multiplicities and classifying the indecomposable Young permutation modules

Details Young module multiplicities and classifying the indecomposable Young permutation modules Young module multiplicities and classifying the indecomposable Young permutation modules

2012-03-28

arxiv.org/abs/1203.6370v1

Mathematics

Representation Theory

22 pages

Scientific paper

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.

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