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arXiv · 0806.1791

Planar Algebra of the Subgroup-Subfactor

Ved Prakash Gupta
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Abstract

We give an identification between the planar algebra of the subgroup-subfactor $R \rtimes H \subset R \rtimes G$ 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 $R \rtimes H \subset R \rtimes G$ 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 $.

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Ved Prakash Gupta. 2008-06-11. Planar Algebra of the Subgroup-Subfactor. https://arxiv.org/abs/0806.1791

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