Trihedral Soergel bimodules
Marco Mackaay, Volodymyr Mazorchuk, Vanessa Miemietz, Daniel Tubbenhauer
Fundamenta Mathematicae 248 (2020), 219-300
MSC: Primary 20C08; Secondary 17B10, 18D05, 18D10, 20F55.
DOI: 10.4064/fm566-3-2019
Opublikowany online: 19 September 2019
Streszczenie
The quantum Satake correspondence relates dihedral Soergel bimodules to the semisimple quotient of the quantum $\mathfrak {sl}_2$ representation category. It also establishes a precise relation between the simple transitive $2$-representations of both monoidal categories, which are indexed by bicolored $\mathsf {ADE}$ Dynkin diagrams.
Using the quantum Satake correspondence between affine $\mathsf {A}_{2}$ Soergel bimodules and the semisimple quotient of the quantum $\mathfrak {sl}_3$ 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 $\mathsf {ADE}$ Dynkin diagrams.
Autorzy
- Marco MackaayCenter for Mathematical Analysis, Geometry,
and Dynamical Systems
Departamento de Matemática
Instituto Superior Técnico
1049-001 Lisboa, Portugal
and
Departamento de Matemática, FCT
Universidade do Algarve
Campus de Gambelas
8005-139 Faro, Portugal
e-mail
- Volodymyr MazorchukDepartment of Mathematics
Uppsala University
Box 480
SE-75106, Uppsala, Sweden
e-mail
- Vanessa MiemietzSchool of Mathematics
University of East Anglia
Norwich NR4 7TJ, United Kingdom
e-mail
- Daniel TubbenhauerInstitut für Mathematik
Universität Zürich
Winterthurerstrasse 190
Campus Irchel, Office Y27J32
CH-8057 Zürich, Switzerland
e-mail
