Diagrammatics for Soergel categories
Ben Elias, Mikhail Khovanov

TL;DR
This paper introduces a diagrammatic presentation of the monoidal category of Soergel bimodules for the symmetric group, providing a visual and algebraic framework for understanding their structure.
Contribution
It develops a planar diagrammatic calculus for Soergel bimodules specifically for the symmetric group, enhancing the understanding of their categorification of the Hecke algebra.
Findings
Diagrammatic presentation of Soergel bimodules for symmetric group
Simplified visualization of bimodule relations
Facilitates computations in categorification context
Abstract
The monoidal category of Soergel bimodules can be thought of as a categorification of the Hecke algebra of a finite Weyl group. We present this category, when the Weyl group is the symmetric group, in the language of planar diagrams with local generators and local defining relations.
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