Clasp technology to knot homology via the affine Grassmannian

Abstract

We categorify all the Reshetikhin-Turaev tangle invariants of type A. Our main tool is a categorification of the generalized Jones-Wenzl projectors (a.k.a. clasps) as infinite twists. Applying this to certain convolution product varieties on the affine Grassmannian we extend our earlier work with Kamnitzer from standard to arbitrary representations.

46 pages. Shortened exposition and simplified some arguments

References in corpus (4)

• 2-Kac-Moody algebras
• Category O and sl(k) link invariants
• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
• Indecomposable 1-morphisms of \dot{U}^+_3 and the canonical basis of U_q^+(sl_3)

Cited by in corpus (8)

• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
• The ${\mathfrak{sl}}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
• Categorified skew Howe duality and comparison of knot homologies
• Rigidity in higher representation theory
• Annular Evaluation and Link Homology
• An Exceptional Collection For Khovanov Homology
• The sl(N)-web algebras and dual canonical bases
• On stable sl3-homology of torus knots