15/09/2016, 14:00 — 14:50 — Room 6.2.38, Faculty of Sciences of the Universidade de Lisboa
Marco Mackaay, Universidade do Algarve
2-Representations of Soergel bimodules in finite Coxeter type
In the last 10-15 years, various people for various reasons have defined and studied interesting examples of 2-categories and their 2-representations. On the Grothendieck group level the main ones correspond to quantum ground and their irreducible representations (or tensor products of those) and Hecke algebras and their cell representations (mostly not irreducible).
With these examples in mind, Mazorchuk and Miemietz set up a general framework for 2-representation theory of 2-categories. In this theory, the role of the simples is played by the so-called simple transitive 2-representations. Unlike the simples of a (finite dimensional) algebra, the simple transitive 2-representations of a (finitary) 2-category are hard to classify in general.
For any Coveter type, the so called Soergel bimodules form a monoidal category (i.e. a 2 category with one object) whose split Grothendieck group is isomorphic to the corresponding Hecke algebra. In this talk, I will explain the classification of the simple transitive 2-representations of (the small quotient of) the 2-category of Soergel bimodules in any finite Coxeter type (joint with Kildetoft-Mazorchuk-Zimmermann and with Tubbenhauer).
