# Simple transitive $2$-representations of Soergel bimodules for finite Coxeter types

## TL;DR

This paper proves that for finite Coxeter types, Soergel bimodules have finitely many simple transitive 2-representations and completes their classification for most types.

## Contribution

It provides a classification of simple transitive 2-representations of Soergel bimodules for finite Coxeter types, except H3 and H4.

## Key findings

- Finite Coxeter types have finitely many simple transitive 2-representations.
- Complete classification achieved for all types but H3 and H4.

## Abstract

In this paper we show that Soergel bimodules for finite Coxeter types have only finitely many equivalence classes of simple transitive $2$-representations and we complete their classification in all types but $H_{3}$ and $H_{4}$.