Towards a Diagrammatic Analogue of the Reshetikhin-Turaev Link Invariants
Abstract
By considering spaces of directed Jacobi diagrams, we construct a diagrammatic version of the Etingof-Kazhdan quantization of complex semisimple Lie algebras. This diagrammatic quantization is used to provide a construction of a directed version of the Kontsevich integral, denoted ZEK, in a way which is analogous to the construction of the Reshetikhin-Turaev invariants from the R-matrices of the Drinfel'd-Jimbo quantum groups. Based on this analogy, we conjecture (and prove in a restricted sense) a formula for the value of the invariant ZEK on the unknot. This formula is simpler than the Wheels formula of [BGRT], but the precise relationship between the two is yet unknown.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.