|Title||Unitary representations of the Thompson group constructed with a category/functor method due to Jones.|
|Presenter||Arnaud Brothier (UNSW Sydney)|
|Author(s)||Dr Arnaud Brothier|
|Session||Functional Analysis, Operator Algebra, Non-commutative Geometry|
The Thompson group is the group of homeomorphisms of [0,1] that are piecewise linear with slopes a power of 2 and breakpoints a dyadic rational. It is one of the most studied discrete group which still remains very mysterious. Motivating in constructing conformal field theories Jones recently discovered a very general process that produces a unitary representation of the Thompson group from very few data such as an isometry between Hilbert spaces or a planar algebra together with a certain element. We will present this construction and provide concrete examples. This is a joint work with Jones.