A special class of prime ideals for infinite symmetric group algebras
Representation Theory
2026-05-18 v2 Group Theory
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.
Keywords
Cite
@article{arxiv.2507.03309,
title = {A special class of prime ideals for infinite symmetric group algebras},
author = {Kevin Coulembier},
journal= {arXiv preprint arXiv:2507.03309},
year = {2026}
}