QGM seminar by Hans Wenzl (University of California at San Diego)

Title: TQFTs from braid group representations

2017.09.25 | Jane Jamshidi

Date Thu 12 Oct
Time 16:30 17:30
Location 1531-215 (Aud. D3)


The finite dimensional representations for Lie type A were originally obtained via Schur-Weyl duality. In particular, the corresponding representation category could be described in terms of the symmetric groups. 

In the quantum setting, the symmetric groups are replaced by braid groups. Unlike in the classical case, braid groups can be used to also describe representation categories of all classical Lie types. This has been known for the categories generated by the vector representation for some time. For spinor representations this was done more recently in connection with certain coideal sub algebras of quantum groups. These results have several applications, among them elementary constructions of TQFTs. Moreover, they also allow to identify TQFTs constructed via other methods.

We discuss the recent progress for spinor representations and the current situation for exceptional Lie types.