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arXiv · 2507.03309

A special class of prime ideals for infinite symmetric group algebras

Kevin Coulembier
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Abstract

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. 2025-07-04. A special class of prime ideals for infinite symmetric group algebras. https://arxiv.org/abs/2507.03309

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