Simple transitive 2-representations of small quotients of Soergel bimodules

Tobias Kildetoft; Marco Mackaay; Volodymyr Mazorchuk; Jakob Zimmermann

paper

Simple transitive 2-representations of small quotients of Soergel bimodules

arXiv:1605.01373

Abstract

In all finite Coxeter types but $I_{2} (12)$ , $I_{2} (18)$ and $I_{2} (30)$ , we classify simple transitive $2$ -rep\-re\-sen\-ta\-ti\-ons for the quotient of the $2$ -category of Soergel bimodules over the coinvariant algebra which is associated to the two-sided cell that is the closest one to the two-sided cell containing the identity element. It turns out that, in most of the cases, simple transitive $2$ -representations are exhausted by cell $2$ -representations. However, in Coxeter types $I_{2} (2 k)$ , where $k \geq 3$ , there exist simple transitive $2$ -representations which are not equivalent to cell $2$ -representations.

Revised version to appear in Trans. AMS