# Extremal weight projectors and categorification of skein algebras

The Temperley-Lieb algebra gives a diagrammatic presentation of the representation category of quantum sl(2), with the famous Jones-Wenzl projectors encoding projections onto finite-dimensional irreducibles. I will talk about a related diagrammatic calculus, in which the Jones-Wenzl projectors decompose further into extremal weight projectors'', and then explain how this might help to categorify skein algebras using link homology technology as developed by Khovanov and others. This is joint work with Hoel Queffelec.