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.
- 2-representation theory
- Hecke algebras
- Quantum groups and their fusion categories
- Soergel bimodules
- Zigzag algebras