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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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