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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