Drinfeld center of planar algebra

Details Drinfeld center of planar algebra Drinfeld center of planar algebra

2012-03-18

arxiv.org/abs/1203.3958v1

Mathematics

Quantum Algebra

Scientific paper

We introduce fusion and contragadient of affine representations of a 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 Hilbert affine representations of $P$ satisfying certain finiteness criterion. As a consequence, we prove Kevin Walker's conjecture for planar algebras.

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