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Soergel Diagrammatics for Dihedral Groups

Elias, Ben

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.

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More About This Work

Academic Units
Mathematics
Thesis Advisors
Khovanov, Mikhail G.
Degree
Ph.D., Columbia University
Published Here
May 17, 2011