Categorified Jones-Wenzl projectors: a comparison (Q2875947)

The Jones-Wenzl projector is an idempotent endomorphism of a tensor power of the natural representation of the quantum group \(U_q(\mathfrak{sl}_2)\). It plays an important role in the definition and construction of Reshetikhin-Turaev invariants of \(3\)-manifolds.NEWLINENEWLINEIn this paper the authors compare the Lie theoretic and topological categorifications of the Jones-Wenzl projector and explicitly describe the relationship between the two. They also show how the Lie theoretic categorification of the Jones-Wenzl projector can be used to categorify the colored Jones polynomial using a certain cabling procedure starting from a categorification of the ordinary Jones polynomial.NEWLINENEWLINEFor the entire collection see [Zbl 1285.00037].