Temperley-Lieb algebras and representation theory (abstract)

From ScottWiki

The Temperley-Lieb algebra naturally arises when studying subfactors. On the other hand, it is intimately connected with $\mathfrak{sl}_2$ representation theory, and its quantum analogues. I'll explain this connection in some detail, and say something about the relationship between these two approaches. Along the way, there'll be a diagrammatic version of the representation theory of the Temperley-Lieb algebra, and an explanation of the Jones polynomial in terms of $\mathfrak{sl}_2$.