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The two-color Soergel calculus.
- Source :
-
Compositio Mathematica . Feb2016, Vol. 152 Issue 2, p327-398. 72p. - Publication Year :
- 2016
-
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 $\mathfrak{sl}_{2}$. 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 $W$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0010437X
- Volume :
- 152
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Compositio Mathematica
- Publication Type :
- Academic Journal
- Accession number :
- 113218140
- Full Text :
- https://doi.org/10.1112/S0010437X15007587