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arXiv · 1308.6611

The two-color Soergel calculus

Ben Elias
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Abstract

We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W . 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 infinite, the parameter q of the Temperley-Lieb algebra may be generic, yielding a quantum version of the geometric Satake equivalence for sl(2). When W is finite, q must be specialized to 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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Ben Elias. 2016-03-05. The two-color Soergel calculus. https://doi.org/10.1112/s0010437x15007587

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