On intermediate subfactors of Goodman-de la Harpe-Jones subfactors

TL;DR

This paper proposes a conjecture on intermediate subfactors generalizing Wall's conjecture, determines all such subfactors for Goodman-Harpe-Jones subfactors, and verifies the conjecture while providing a negative answer to a related question.

Contribution

It introduces a new conjecture on intermediate subfactors, classifies all intermediate subfactors of Goodman-Harpe-Jones subfactors, and addresses related questions in the field.

Findings

Verification of the conjecture for Goodman-Harpe-Jones subfactors

Complete classification of intermediate subfactors in this context

Negative answer to a question related to the conjecture

Abstract

In this paper we present a conjecture on intermediate subfactors which is a generalization of Wall's conjecture from the theory of finite groups. Motivated by this conjecture, we determine all intermediate subfactors of Goodman-Harpe-Jones subfactors, and as a result we verify that Goodman-Harpe-Jones subfactors verify our conjecture. Our result also gives a negative answer to a question motivated by a conjecture of Aschbacher-Guralnick.