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.
Soergel Calculus
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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 of Soergel's classification of the indecomposable Soergel bimodules.
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math.CT 1years
2024 1verdicts
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Asymptotics in infinite monoidal categories
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.