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Characters of odd degree of symmetric groups. (English) Zbl 1434.20007
Summary: We construct a natural bijection between odd-degree irreducible characters of \(\mathfrak{S}_{2^n}\) and linear characters of its Sylow 2-subgroup \(P_{2^n}\). We show that such a bijection is nicely induced by the restriction functor. We conclude with a characterization of the irreducible characters \(\chi\) of \(\mathfrak{S}_n\) such that the restriction of \(\chi\) to \(P_n\) has a unique linear constituent.

MSC:
20C30 Representations of finite symmetric groups
20C15 Ordinary representations and characters
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