Characters of odd degree of symmetric groups
Representation Theory
2017-05-17 v2 Group Theory
Abstract
We construct a natural bijection between odd-degree irreducible characters of S_n and linear characters of its Sylow 2-subgroup P_n. When n is a power of 2, we show that such a bijection is nicely induced by the restriction functor. We conclude with a characterization of the irreducible characters \chi of S_n such that the restriction of \chi to P_n has a unique linear constituent.
Keywords
Cite
@article{arxiv.1601.03839,
title = {Characters of odd degree of symmetric groups},
author = {Eugenio Giannelli},
journal= {arXiv preprint arXiv:1601.03839},
year = {2017}
}