Flatness and fusion coefficients

Vijay Kodiyalam and V.S. Sunder

Vol. 201 (2001), No. 1, 177–204

DOI: 10.2140/pjm.2001.201.177

Abstract

This paper addresses the problem of how to directly read off the ‘fusion coefficients’ (for the tensor-products of bimodules arising in the ‘tower of the basic construction’) for a subfactor, from the data of the associated paragroup. The solution to this problem is closely related to a reformulation, which is obtained here, of the flatness condition to be satisfied by the connection on a paragroup; our reformulation is best described by the phrase ‘1 ∗ flatness’, in contrast with Ocneanu’s initial formulation as ‘4 ∗ flatness’ and Kawahigashi’s subsequent reformulation as ‘2 ∗ flatness’.

Milestones

Received: 10 November 1999

Revised: 31 July 2000

Published: 1 November 2001