Planar Algebra of the Subgroup-Subfactor[HBNI Th1]

Abstract

An identification between the planar algebra of the subgroup-subfactor R x H subset of R x G is given and the G-invariant planar subalgebra of the planar algebra of the bipartite graph *n (the graph with 1 odd and n even vertices), where n = [G:H]. The crucial step in this identification process is the exhibition of a model for the basic construction tower, and thereafter of the standard invariant, of R x H subset of R x G, interms of operator matrices. The relationship between Jones' Planar algebra and Ocneanu's paragroup approaches to the standard invariant.