Diagrammatics for Soergel categories

Abstract

The monoidal category of Soergel bimodules can be thought of as a categorification of the Hecke algebra of a finite Weyl group. We present this category, when the Weyl group is the symmetric group, in the language of planar diagrams with local generators and local defining relations.

long awaited update to published version

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Cited by in corpus (41)

• The two-color Soergel calculus
• Higher-Dimensional Algebra VII: Groupoidification
• An introduction to diagrammatic algebra and categorified quantum sl(2)
• An approach to categorification of some small quantum groups II
• Schubert calculus and torsion explosion
• Categorifying fractional Euler characteristics, Jones-Wenzl projector and $3j$-symbols
• Categorifications from planar diagrammatics
• Legendrian Weaves: N-graph Calculus, Flag Moduli and Applications
• Trace decategorification of the Hecke category
• Categorified Young symmetrizers and stable homology of torus links
• Modular representation theory in type A via Soergel bimodules
• Diagram categories for ${\text{U}}_q$-tilting modules at roots of unity
• Standard objects in 2-braid groups
• A categorical action on quantized quiver varieties
• On generalized category $\mathcal{O}$ for a quiver variety
• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Khovanov polynomials for satellites and asymptotic adjoint polynomials
• Soergel calculus and Schubert calculus
• Blob algebra approach to modular representation theory
• The Hecke Bicategory
• Rouquier Complexes are Functorial over Braid Cobordisms
• Monoidal categories, representation gap and cryptography
• Khovanov-Rozansky homology via Cohen-Macaulay approximations and Soergel bimodules
• On some $p$-differential graded link homologies
• Koszul Duality and Soergel Bimodules for Dihedral Groups
• Diagrammatics for Coxeter groups and their braid groups
• Colored Khovanov-Rozansky homology for infinite braids
• Integral HOMFLY-PT and sl(n)-link homology
• Localized calculus for the Hecke category
• Blob algebra and two-color Soergel calculus
• Cellularity of the p-Canonical Basis for Symmetric Groups
• Braid group actions from categorical symmetric Howe duality on deformed Webster algebras
• Planar diagrammatics of self-adjoint functors and recognizable tree series
• Trivalent vertices and bordered knot Floer homology in the standard basis
• Actions of sl_2 on algebras appearing in categorification
• K-theory Soergel Bimodules
• Categorifying Hecke algebras at prime roots of unity, part I
• Ext-enhanced monoidal Koszul duality for ${\mathrm{GL}}_2$
• Twisted actions on cohomologies and bimodules
• Jucys-Murphy elements for Soergel bimodules
• A diagram algebra for Soergel modules corresponding to smooth Schubert varieties