Planar Algebra of the Subgroup-Subfactor

Abstract

We give an identification between the planar algebra of the subgroup-subfactor $R⋊H\subset R⋊G$ and the $G$-invariant planar subalgebra of the planar algebra of the bipartite graph ${\star }_n$, where $n=[G:H]$. The crucial step in this identification is an exhibition of a model for the basic construction tower, and thereafter of the standard invariant, of $R⋊H\subset R⋊G$ in terms of operator matrices. We also obtain an identification between the planar algebra of the fixed algebra subfactor $R^G\subset R^H$ and the $G$-invariant planar subalgebra of the planar algebra of the `flip' of ${\star }_n$.

30 pages

Cited by in corpus (1)

• A2-Planar Algebras II: Planar Modules