Publikace na Matematicko-fyzikální fakulta |
2014
Abstrakt
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.