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

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

doi:10.1112/plms.12515

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

Representation Theory 2023-08-17 v3 Category Theory Quantum Algebra

Authors: Marco Mackaay , Volodymyr Mazorchuk , Vanessa Miemietz , Daniel Tubbenhauer , Xiaoting Zhang

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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 $H_{4}$ .

Keywords

Soergel bimodules finite Coxeter types simple transitive 2-representations classification representation theory

Cite

@article{arxiv.1906.11468,
  title  = {Simple transitive $2$-representations of Soergel bimodules for finite Coxeter types},
  author = {Marco Mackaay and Volodymyr Mazorchuk and Vanessa Miemietz and Daniel Tubbenhauer and Xiaoting Zhang},
  journal= {arXiv preprint arXiv:1906.11468},
  year   = {2023}
}

Comments

Final version, to appear in the Proceedings of the LMS

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

Abstract

Keywords

Cite

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