Simple transitive $2$-representations of Soergel bimodules for finite Coxeter types

Daniel Tubbenhauer; Marco Mackaay; Vanessa Miemietz; Volodymyr Mazorchuk; Xiaoting Zhang

Simple transitive $2$-representations of Soergel bimodules for finite Coxeter types

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arxiv 1906.11468 v3 pith:4LN7SDIS submitted 2019-06-27 math.RT math.CTmath.QA

Marco Mackaay , Volodymyr Mazorchuk , Vanessa Miemietz , Daniel Tubbenhauer , Xiaoting Zhang This is my paper · ORCID

classification math.RTmath.CTmath.QA

keywords typesbimodulescoxeterfiniterepresentationssimplesoergeltransitive

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abstract

In this paper we show that Soergel bimodules for finite Coxeter types have only finitely many equivalence classes of simple transitive $2$-representations and we complete their classification in all types but $H_{3}$ and $H_{4}$.

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Idempotents, traces, and dimensions in Hecke categories
math.RT 2025-07 conditional novelty 8.0 of 10

The paper provides closed formulas for recursible local intersection forms and recursive partial trace formulas that reduce categorical dimensions in asymptotic Hecke categories to diagrammatic computations.

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