Drinfeld center of planar algebra

Abstract

We introduce fusion, contragradient and braiding of Hilbert affine representations of a subfactor planar algebra $P$ (not necessarily having finite depth). We prove that if $N\subset M$ is a subfactor realization of $P$, then the Drinfeld center of the $N$-$N$-bimodule category generated by ${}_N{L}^2(M{)}_M$, is equivalent to the category of Hilbert affine representations of $P$ satisfying certain finiteness criterion. As a consequence, we prove Kevin Walker's conjecture for planar algebras.

32 pages

References in corpus (2)

• A planar calculus for infinite index subfactors
• On the planar algebra of Ocneanu's asymptotic inclusion

Cited by in corpus (3)

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