Gentle introduction to Soergel bimodules I: The basics

TL;DR

This paper provides an accessible introduction to Soergel bimodules, focusing on basic concepts, calculations, and open problems to help newcomers understand this combinatorial area of algebra.

Contribution

It offers the first introductory, combinatorial overview of Soergel bimodules, emphasizing foundational understanding and setting the stage for future research.

Findings

Introduces basic concepts of Soergel bimodules

Provides methods for calculating with bimodules

Highlights open problems in the field

Abstract

This paper is the first of a series of introductory papers on the fascinating world of Soergel bimodules. It is combinatorial in nature and should be accessible to a broad audience. The objective of this paper is to help the reader feel comfortable calculating with Soergel bimodules and to explain some of the important open problems in the field. The motivations, history and relations to other fields will be developed in subsequent papers of this series.