Jones's planar-algebraic Walker conjecture for finite-depth subfactors

Let NMN\subset M be a finite-depth subfactor, let PP be its associated subfactor planar algebra, and let the NN-NN-bimodule category generated by NL2(M)M_N L^2(M)_M be the category whose Drinfeld center is under consideration. Jones's planar-algebraic Walker conjecture. The category of locally finite Hilbert affine representations of PP is equivalent to the Drinfeld center of the NN-NN-bimodule category generated by NL2(M)M_N L^2(M)_M.

This is the planar-algebra formulation of the preceding Walker conjecture, motivated by the finite-group subfactor case, where the relevant bimodule category is equivalent to the representation category of a finite group's quantum double. The supplied text does not state whether the finite-depth formulation is resolved.

Sources & referencesView supporting material

Primary source

Paramita Das, Shamindra Kumar Ghosh and Ved Prakash Gupta, “Drinfeld center of planar algebra”, arXiv:1203.3958 (2014).

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