Ore's theorem on subfactor planar algebras
Operator Algebras
2023-06-06 v5 Combinatorics
Group Theory
Quantum Algebra
Representation Theory
Abstract
This article proves that an irreducible subfactor planar algebra with a distributive biprojection lattice admits a minimal 2-box projection generating the identity biprojection. It is a generalization (conjectured in 2013) of a theorem of Oystein Ore on distributive intervals of finite groups (1938), and a corollary of a natural subfactor extension of a conjecture of Kenneth S. Brown in algebraic combinatorics (2000). We deduce a link between combinatorics and representations in finite group theory.
Cite
@article{arxiv.1704.00745,
title = {Ore's theorem on subfactor planar algebras},
author = {Sebastien Palcoux},
journal= {arXiv preprint arXiv:1704.00745},
year = {2023}
}
Comments
14 pages. It reproduces some preliminaries of arXiv:1702.02124 and arXiv:1703.04486, for being self-contained