A categorification of quantum $\mathfrak{sl}_3$ projectors and the $\mathfrak{sl}_3$ Reshetikhin–Turaev invariant of tangles

Abstract

We construct a categorification of the quantum $\mathfrak{sl}_3$ projectors, the $\mathfrak{sl}_3$ analog of the Jones–Wenzl projectors, as the stable limit of the complexes assigned to $k$-twist torus braids (as $k \to \infty$) in a suitably shifted version of Morrison and Nieh’s geometric formulation of $\mathfrak{sl}_3$ link homology [14] We use these projectors to give a categorification of the $\mathfrak{sl}_3$ Reshetikhin–Turaev invariant of framed tangles.