# A rigidity result for normalized subfactors

## TL;DR

This paper proves a rigidity theorem for subfactors normalized by lattice representations in higher rank Lie groups, showing such subfactors are either trivial or of finite index.

## Contribution

It establishes a new rigidity result for normalized subfactors in the context of higher rank simple Lie groups and their lattices.

## Key findings

- Normalized subfactors are either trivial or of finite index
- Subfactors of $L ext{ extbackslash}Gamma$ normalized by $ ext{ extbackslash}Gamma$ are classified
- The result applies to subfactors associated with lattices in higher rank Lie groups

## Abstract

We show a rigidity result for subfactors that are normalized by a representation of a lattice $\Gamma$ in a higher rank simple Lie group with trivial center into a finite factor. This implies that every subfactor of $L\Gamma$ which is normalized by the natural copy of $\Gamma$ is trivial or of finite index.