Gentle introduction to Soergel bimodules I: The basics

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.