Centralizers of the infinite symmetric group

Abstract

We review and introduce several approaches to the study of centralizer algebras of the infinite symmetric group $S_{\infty }$. Our study is led by the double commutant relationships between finite symmetric groups and partition algebras; each approach produces a centralizer algebra that is contained in a partition algebra. Our goal is to incorporate invariants of $S_{\infty }$, which ties our work to the study of symmetric functions in non-commuting variables. We resultantly explore sequence spaces as permutation modules, which yields families of non-unitary representations of $S_{\infty }$.

References in corpus (2)

• FI-modules and stability for representations of symmetric groups
• Stability patterns in representation theory