The Soergel category and the redotted Webster algebra

TL;DR

This paper introduces graded rings related to Webster algebras and singular Soergel bimodules, and constructs a categorical braid group action that categorifies the Burau representation, advancing the understanding of categorification in algebra.

Contribution

It constructs a new collection of graded rings linked to Webster algebras and develops a categorical braid group action for categorifying the Burau representation.

Findings

Graded rings surject onto Webster rings for sl(2).

Categorical braid group action constructed.

Connections to singular Soergel bimodules established.

Abstract

We describe a collection of graded rings which surject onto Webster rings for sl(2) and which should be related to certain categories of singular Soergel bimodules. In the first non-trivial case, we construct a categorical braid group action which categorifies the Burau representation.