Intermediate planar algebra revisited, II

TL;DR

This paper revisits the structure of intermediate subfactor planar algebras within extremal subfactors of finite index, extending previous work to cases without irreducibility assumptions.

Contribution

It provides a detailed description of the subfactor planar algebra for intermediate subfactors in a more general setting, relaxing irreducibility constraints.

Findings

Characterization of intermediate subfactor planar algebras

Extension of previous results to non-irreducible cases

Enhanced understanding of subfactor structures

Abstract

We describe the subfactor planar algebra of an intermediate subfactor $N\subset Q \subset M$ of an extremal subfactor $N\subset M$ of finite Jones index which is not necessarily irreducible.