This analysis identifies prime ideals in symmetric group algebras, suggesting new links with tensor categories and representations.
We identify an interesting special class of prime ideals in the finitary infinite symmetric group algebra. We show that the set of such ideals carries a semiring structure. Over the complex numbers, we establish a connection with spherical representations of (the Gelfand pair corresponding to) the infinite symmetric group. In positive characteristic, we investigate a close connection with the structure theory of symmetric tensor categories.
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Kevin Coulembier (2025) studied this question.