Ore's theorem on subfactor planar algebras
Abstract
This article proves that an irreducible subfactor planar algebra with a distributive biprojection lattice admits a minimal 2box 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2017
 arXiv:
 arXiv:1704.00745
 Bibcode:
 2017arXiv170400745P
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Combinatorics;
 Mathematics  Group Theory;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory;
 05E15;
 46L37 (Primary) 06D10;
 20C15;
 05E10 (Secondary)
 EPrint:
 14 pages. It reproduces some preliminaries of arXiv:1702.02124 and arXiv:1703.04486, for being selfcontained