David Penneys
Abstract:
We classify subfactors by three invariants of increasing complexity: the index, the principal graph, and the standard invariant. The standard invariant is a unitary 2-category which generalizes the representation category of a (quantum) group, and thus we think of subfactors as objects which encode quantum symmetries. In one sense, subfactors of small index are the simplest examples of subfactors, and we have a complete classification of their standard invariants to index 5.
I will discuss recent joint work with Liu and Morrison which classifies standard invariants of 1-supertransitive subfactors without intermediates with index in $(3+\sqrt{5},6.2)$. We show there are exactly 3 examples corresponding to $SO(3)_q$ at a root of unity and two "twisted" variations.
University of Toronto
Mon, 17/03/2014 - 12:00pm
RC-4082, The Red Centre, UNSW