Linear Analysis Seminar

Date: January 30, 2018

Time: 2:00PM - 3:00PM

Location: BLOC 220

Speaker: Dave Penneys, Ohio State

Title: Standard invariants for discrete subfactors

Abstract: The standard invariant of a finite index II_1 subfactor is a $\lambda$-lattice and forms a planar algebra. In turn, the planar algebra formalism has been helpful in constructing and classifying subfactors, as well as studying analytic properties. In joint work with Corey Jones, we give a well-behaved notion of the standard invariant of an extremal irreducible discrete subfactor $N\subset M$, where $N$ is type II_1 and $M$ is an arbitrary factor. We also get a subfactor reconstruction theorem. This generalizes the standard invariant for finite index subfactors to a natural class of infinite index subfactors. Particular examples include the symmetric enveloping inclusion and examples coming from discrete quantum groups.