A special class of prime ideals for infinite symmetric group algebras

2025/07/04 by Kevin Coulembier, Coulembier, Kevin · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2507.03309

openalex publication_date 2025/07/04 · openalex created_date 2025/10/20 · openalex updated_date 2026/07/28

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.

Citations

• Tensor ideals of abelian type and quantum groups
• Rigidity of non-negligible objects of moderate growth in braided categories
• Inductive systems of the symmetric group, polynomial functors and tensor categories
• Incompressible tensor categories
• Super invariant theory in positive characteristic
• On Frobenius exact symmetric tensor categories
• New incompressible symmetric tensor categories in positive characteristic
• On the Frobenius functor for symmetric tensor categories in positive\n characteristic
• Symmetric tensor categories in characteristic 2
• On symmetric fusion categories in positive characteristic
• On the representations of the infinite symmetric group

Cited by

• Tensor ideals of abelian type and quantum groups

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