Characters of odd degree of symmetric groups

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 χof S_n such that the restriction of χto P_n has a unique linear constituent.

References in corpus (2)

• Odd partitions in Young's lattice
• Restriction of odd degree characters and natural correspondences

Cited by in corpus (6)

• Sylow branching coefficients for symmetric groups
• Non-linear Sylow branching coefficients for symmetric groups
• Restriction of odd degree characters and natural correspondences
• Macdonald trees and determinants of representations for finite Coxeter groups
• A note on restriction of Characters of Alternating groups to Sylow Subgroups
• The Representation Theory of 2-Sylow Subgroups of the Symmetric Group