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arXiv · 1601.03839

Characters of odd degree of symmetric groups

Eugenio Giannelli
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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.

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Eugenio Giannelli. 2016-01-25. Characters of odd degree of symmetric groups. https://doi.org/10.1112/jlms.12048

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