Soergel Diagrammatics for Dihedral Groups

We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W, finite or infinite. The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The indecomposable Soergel bimodules are the images of Jones-Wenzl projectors. When W is finite, the Temperley-Lieb category must be taken at an appropriate root of unity, and the negligible Jones-Wenzl projector yields the Soergel bimodule for the longest element of W.

Author dc:creator

• Elias, Ben

• Mathematics
• Hecke algebras
• Weyl groups

Language dc:language

English

DOI dc:identifier

https://doi.org/10.7916/D8C82H96

OAI identifier oai:identifier

oai:academiccommons.columbia.edu:10.7916/D8C82H96