We construct a natural bijection between odd-degree irreducible characters of S2n and linear characters of its Sylow 2-subgroup P2n . We show that such a bijection is nicely induced by the restriction functor. We conclude with a characterization of the irreducible characters χ of Sn such that the restriction of χ to Pn has a unique linear constituent.
Characters of odd degree of symmetric groups / giannelli eugenio. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 96:(2017), pp. 1-14. [10.1112/jlms.12048]
Characters of odd degree of symmetric groups
giannelli eugenio
2017
Abstract
We construct a natural bijection between odd-degree irreducible characters of S2n and linear characters of its Sylow 2-subgroup P2n . We show that such a bijection is nicely induced by the restriction functor. We conclude with a characterization of the irreducible characters χ of Sn such that the restriction of χ to Pn has a unique linear constituent.
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