Simple commutative algebras in Deligne's categories Rep(Sₜ)

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We show that in the Deligne categories Rep(Sₜ) for t a transcendental number, the only simple algebra objects are images of simple algebras in the category of representations of a symmetric group under a canonical induction functor. They come in families which interpolate the families of algebras of functions on the cosets of H× Sₙ₋ₖ in Sₙ, for a fixed subgroup H of Sₖ.