Characters of odd degree of symmetric groups
Abstract
We construct a natural bijection between odd-degree irreducible characters of Sn and linear characters of its Sylow 2-subgroup Pn. 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 of Sn such that the restriction of to Pn has a unique linear constituent.
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