October 20, 2025Open Access

A special class of prime ideals for infinite symmetric group algebras

Key Points

A special class of prime ideals was identified, establishing a novel semiring structure within infinite symmetric group algebras.
Over complex numbers, connections to spherical representations related to the infinite symmetric group were explored.
In positive characteristic, findings showed significant ties between prime ideals and the structure theory of symmetric tensor categories.
This work emphasizes the importance of prime ideals in understanding the algebraic properties of group representations.

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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Cite This Study

Kevin Coulembier (Fri,) studied this question.

synapsesocial.com/papers/68f5fcdc8d54a28a75cf24ae https://doi.org/https://doi.org/10.48550/arxiv.2507.03309

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