Planar algebra of the subgroup-subfactor |
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Authors: | Ved Prakash Gupta |
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Institution: | (1) The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600 113, India |
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Abstract: | We give an identification between the planar algebra of the subgroupsubfactor R ⋊ H ⊂ R ⋊ G and the G-invariant planar subalgebra of the planar algebra of the bipartite graph ★
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 ⊂ R ⋊ G in terms of operator matrices.
We also obtain an identification between the planar algebra of the fixed algebra subfactor R
G
⊂ R
H
and the G-invariant planar subalgebra of the planar algebra of the ‘flip’ of ★
n
. |
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Keywords: | Planar algebras subfactors standard invariant |
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