A Categorification of Quantum sl_3 Projectors and the sl_3 Reshetikhin-Turaev Invariant of Tangles

Abstract

We construct a categorification of the quantum sl_3 projectors, the sl_3 analog of the Jones-Wenzl projectors, as the stable limit of the complexes assigned to k-twist torus braids (as k goes to infinity) in a suitably shifted version of Morrison and Nieh's geometric formulation of sl_3 link homology (math.GT/0612754). We use these projectors to give a categorification of the sl_3 Reshetikhin-Turaev invariant of framed tangles.

56 pages, several figures; final version, which appears in Quantum Topology. v2 corrects several typos, includes additional figures, expands on Examples 5.4 and 5.5, and corrects an error in Example 5.4

References in corpus (3)

• A Diagrammatic Category for the Representation Theory of U_q(sl_n)
• Categorifying fractional Euler characteristics, Jones-Wenzl projector and $3j$-symbols
• A Note on the Grothendieck Group of an Additive Category

Cited by in corpus (8)

• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
• Clasp technology to knot homology via the affine Grassmannian
• Annular Evaluation and Link Homology
• A Note on the Grothendieck Group of an Additive Category
• Skein Modules from Skew Howe Duality and Affine Extensions
• On stable sl3-homology of torus knots
• Khovanov-Rozansky homology for infinite multi-colored braids
• Colored Khovanov-Rozansky homology for infinite braids