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Soergel calculus. (English) Zbl 1427.20006

Summary: 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.

MSC:

20C08 Hecke algebras and their representations
18M05 Monoidal categories, symmetric monoidal categories
20C33 Representations of finite groups of Lie type
20F55 Reflection and Coxeter groups (group-theoretic aspects)
20G05 Representation theory for linear algebraic groups
22E46 Semisimple Lie groups and their representations

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