Thursday, March 13th, 2014
1:00pm - 2:30pm, in McCormack 1-620

Shamindra Ghosh

Indian Statistical Institute

Affine representations of planar algebras II

Abstract: Vaughan Jones described the most important invariant of finite index subfactors by algebra of certain kinds of pictures on the Euclidean plane, which he called 'planar algebras'. One can then look at the representation theory of planar algebras. These representations in a specific case of finite groups, turned out to be in one-to-one correspondence with representations of the quantum double of the group. Analogous results also appeared in the world of TQFTs in the work of Kevin Walker. Based on this analogy, Jones conjectured that the representation category of the planar algebra associated to a finite index, finite depth subfactor is equivalent to Drinfeld center of the bimodule category associated to the subfactor. This will be the second of a two-part talk. We will consider the very basic example of diagonal subfactors which arises from an action of a finitely generated group (not necessarily finite), and then find its affine representations. We will see that various analytic properties of the group can be expressed in terms of the pictures involved. This is a joint work with Ved Prakash Gupta and Paramita Das.