The 2-representation theory of Soergel bimodules of finite Coxeter type: a road map to the complete classification of all simple transitive 2-representations

 I will first recall Lusztig's asymptotic Hecke algebra and its categorification, a fusion category obtained from the perverse homology of Soergel bimodules. For example, for finite dihedral Coxeter type this fusion category is a 2-colored version of the semisimplified quotient of the module category of quantum sl(2) at a root of unity, which Reshetikhin-Turaev and Turaev-Viro used for the construction of 3-dimensional Topological Quantum Field Theories.

In the second part of my talk, I will recall the basics of 2-representation theory and indicate how the fusion categories above can conjecturally be used to study the 2-representation theory of Soergel bimodules of finite Coxeter type.     

This is joint work with Mazorchuk, Miemietz, Tubbenhauer and Zhang.

Date and Venue

Start Date
Venue
Room 1.09

Speaker

Marco Mackaaij

Speaker's Institution

Universidade do Algarve / CAMGSD

Files

Area

Geometry and Topology