English

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.

Keywords

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