Abstract

This paper addresses the problem of how to directly read off the ‘fusion coeficients’ (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’.

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