Pivotal Categories, Planar Algebras and Subfactors 2

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I'll define planar algebras, a notion closely related to pivotal categories, and introduced by Jones as the appropriate formalism for `the standard invariant' of a subfactor. I'll explain in detail how to construct the planar algebra associated to an object in a pivotal category.

This framework suggests an alternative version of Jones' construction of the planar algebra associated to a (extremal, finite index) II_1 subfactor -- first we'll put together a pivotal category, and then use the above construction. I'll go through this in detail, explaining just enough of the subfactor side of the story.

(After this, probably in a subsequent talk, I'll return to my result about generators and relations for Rep(U_q(sl_n)) as a pivotal category.)