Jones-Wenzl idempotents for rank 2 simple Lie algebras

Abstract

Temperley-Lieb algebras have been generalized to web spaces for rank 2 simple Lie algebras. Using these webs, we find a complete description of the Jones-Wenzl idempotents for the quantum $\mathfrak{sl}(3)$ and $\mathfrak{sp}(4)$ by single clasp expansions. We discuss applications of these expansions.