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arxiv: 1309.0865 · v1 · pith:CHH2R2OInew · submitted 2013-09-03 · 🧮 math.QA · math.RT

Soergel Calculus

Ben Elias , Geordie Williamson This is my paper
classification 🧮 math.QA math.RT
keywords soergelcategorybimodulesgivebasiscalculusclassificationdiagrammatics
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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 of Soergel's classification of the indecomposable Soergel bimodules.

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  1. Asymptotics in infinite monoidal categories

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    Formulas are discussed for the asymptotic growth rate of summands in tensor powers in monoidal categories with infinitely many indecomposables, using generalized Perron-Frobenius theory and random walk techniques.