Presentation of right-angled Soergel categories by generators and relations

TL;DR

This paper provides a presentation of the Soergel bimodule category for right-angled Coxeter groups using generators and relations, advancing the understanding of its algebraic structure.

Contribution

It introduces a new presentation of the Soergel bimodule category specifically for right-angled Coxeter groups, using generators and relations.

Findings

Explicit generators and relations for the category

Simplifies understanding of the category's structure

Facilitates computations within the category

Abstract

Soergel bimodule category B is a categorification of the Hecke algebra of a Coxeter system (W,S). We find a presentation of B (as a tensor category) by generators and relations when W is a right-angled Coxeter group.