Categorification of the colored ${\mathfrak{sl}}_3$-invariant

Abstract

We give explicit resolutions of all finite dimensional, simple $U_q(\mathfrak{s}{\mathfrak{l}}_3)$-modules. We use these resolutions to categorify the colored ${\mathfrak{sl}}_3$-invariant of framed links via a complex of complexes of graded $\mathbb{Z}$-modules.

39 pages, many figures. Comments welcome!