Soergel calculus

Elias, Ben; Williamson, Geordie

doi:10.1090/ert/481

Soergel calculus
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by Ben Elias and Geordie Williamson

Represent. Theory 20 (2016), 295-374

DOI: https://doi.org/10.1090/ert/481

Published electronically: October 7, 2016

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Abstract:

The monoidal category of Soergel bimodules is an incarnation of the Hecke category, a fundamental object in representation theory. We present this category by generators and relations, using the language of planar diagrammatics. We show that Libedinsky’s light leaves give a basis for morphism spaces and give a new proof and a generalization of Soergel’s classification of the indecomposable Soergel bimodules.

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