Trihedral Soergel bimodules

Mackaay, Marco; Mazorchuk, Volodymyr; Miemietz, Vanessa; Tubbenhauer, Daniel

http://hdl.handle.net/10400.1/14737

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
Accepted_Manuscript.pdf		1.16 MB	Adobe PDF	Download

Send Feedback

Authors

Abstract(s)

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.