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Trihedral Soergel bimodules


Mackaay, Marco; Mazorchuk, Volodymyr; Miemietz, Vanessa; Tubbenhauer, Daniel (2020). Trihedral Soergel bimodules. Fundamenta Mathematicae, 248(3):219-300.

Abstract

The quantum Satake correspondence relates dihedral Soergel bimodules to the semisimple quotient of the quantum sl2 representation category. It also establishes a precise relation between the simple transitive 2-representations of both monoidal categories, which are indexed by bicolored ADE Dynkin diagrams.
Using the quantum Satake correspondence between affine A2 Soergel bimodules and the semisimple quotient of the quantum sl3 representation category, we introduce trihedral Hecke algebras and Soergel bimodules, generalizing dihedral Hecke algebras and Soergel bimodules. These have their own Kazhdan-Lusztig combinatorics, simple transitive 2-representations corresponding to tricolored generalized ADE Dynkin diagrams.

Abstract

The quantum Satake correspondence relates dihedral Soergel bimodules to the semisimple quotient of the quantum sl2 representation category. It also establishes a precise relation between the simple transitive 2-representations of both monoidal categories, which are indexed by bicolored ADE Dynkin diagrams.
Using the quantum Satake correspondence between affine A2 Soergel bimodules and the semisimple quotient of the quantum sl3 representation category, we introduce trihedral Hecke algebras and Soergel bimodules, generalizing dihedral Hecke algebras and Soergel bimodules. These have their own Kazhdan-Lusztig combinatorics, simple transitive 2-representations corresponding to tricolored generalized ADE Dynkin diagrams.

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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Algebra and Number Theory
Language:English
Date:2020
Deposited On:15 Nov 2021 08:45
Last Modified:26 Apr 2024 01:35
Publisher:Polska Akademia Nauk, Instytut Matematyczny
ISSN:0016-2736
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.4064/fm566-3-2019
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