On subfactors arising from asymptotic representations of symmetric groups

TL;DR

This paper studies subfactors derived from asymptotic representations of infinite symmetric groups, linking their invariants to Thoma parameters, and exploring the structure of stabilizer subgroups.

Contribution

It introduces a method to compute subfactor invariants for infinite symmetric groups using Thoma parameters, connecting group representations to subfactor theory.

Findings

Computed subfactor invariants in terms of Thoma parameters

Established a connection between asymptotic representations and hyperfinite subfactors

Analyzed the structure of stabilizer subgroups in infinite symmetric groups

Abstract

We consider the infinite symmetric group and its infinite index subgroup given as the stabilizer subgroup of one element under the natural action on a countable set. This inclusion of discrete groups induces a hyperfinite subfactor for each finite factorial representation of the larger group. We compute subfactor invariants of this construction in terms of the Thoma parameter.