Trihedral Soergel bimodules

MacKaay, Marco, Mazorchuk, Volodymyr, Miemietz, Vanessa and Tubbenhauer, Daniel (2020) Trihedral Soergel bimodules. Fundamenta Mathematicae, 248 (3). pp. 219-300. ISSN 0016-2736

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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 A 2 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.

Item Type:	Article
Uncontrolled Keywords:	2-representation theory,hecke algebras,quantum groups and their fusion categories,soergel bimodules,zigzag algebras,algebra and number theory ,/dk/atira/pure/subjectarea/asjc/2600/2602
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?... https://arxiv.org/abs/1804.08920
Depositing User:	LivePure Connector
Date Deposited:	21 Mar 2019 01:03
Last Modified:	14 Dec 2024 01:27
URI:	https://ueaeprints.uea.ac.uk/id/eprint/70286
DOI:	10.4064/fm566-3-2019

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