Spectral gap and definability

TL;DR

This paper explores the connection between spectral gap properties in unitary representations and subfactors and the definability of key sets within related mathematical structures, providing multiple applications of this relationship.

Contribution

It establishes a novel link between spectral gap concepts and definability, offering new insights and applications in the study of operator algebras and representation theory.

Findings

Spectral gap implies definability of certain sets.

Applications to operator algebras and subfactor theory.

New characterizations of spectral gap in terms of definability.

Abstract

We relate the notions of spectral gap for unitary representations and subfactors with definability of certain important sets in the corresponding structures. We give several applications of this relationship.