A note on the signature representations of the symmetric groups
Representation Theory
2020-03-17 v2
Abstract
For a partition {\lambda} and a prime p, we prove a necessary and sufficient condition for there exists a composition {\delta} such that {\delta} can be obtained from {\lambda} after rearrangement and all the partial sums of {\delta} are not divisible by p.
Cite
@article{arxiv.1901.05829,
title = {A note on the signature representations of the symmetric groups},
author = {Kay Jin Lim and Jialin Wang},
journal= {arXiv preprint arXiv:1901.05829},
year = {2020}
}
Comments
This is a substantially revised version of previous ones. In the third section, we calculate some explicit p-Kostka numbers