The two-color Soergel calculus
By Ben Elias. Compositio Mathematica, 2013
85 citations recorded by the source corpus.
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 $\mathfrak{sl}_{2}$. 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 $W$.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5d794f49cd93e2a954c5e208eea0f8489a25063f
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
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Citations in the corpus
- Schubert calculus and torsion explosion (2013, background): “ Elias and the author found a presentation for the monoidal category of Soergel bimodules by generators and relations [EW], building on the work of Libedinsky [Lib10], Elias-Khovanov [EK10] and Elias [Eli]. One of the applications of this theory is that one can decide whether a given intersection co”
- The $p$-Canonical Basis for Hecke Algebras (2015, background): “egrees of its vertices and of the degrees of the polynomials decorating its regions. Next, we introduce the diagrammatic category of Soergel bimodules. The main reference for this is [EW13] (see also [Eli13] in the dihedral case and [EK10] in type A). Let H BSbe the strict monoidal category with Z-g”