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YOUNG MODULE MULTIPLICITIES, DECOMPOSITION NUMBERS AND THE INDECOMPOSABLE YOUNG PERMUTATION MODULES

CHRISTOPHER C. GILL

Department of Algebra, Charles University, Sokolovska 83, Praha 8, 186 75, Czech Republic

https://doi.org/10.1142/S0219498813501478Cited by:5 (Source: Crossref)

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 corresponding to adding multiples of a p-power to the first row of a partition.

Keywords:

AMSC: 20C30

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