# Gustav Lehrer (University of Sydney)

## The Temperley-Lieb tangle category of type B and some infinite dimensional representations of quantum $$\mathfrak{sl}_2$$

I shall present an equivalence of categories between the type B Temperley-Lieb category, realised as a subquotient of the classical category of unoriented tangles, and a category of projective infinite dimensional representations of quantum $$\mathfrak{sl}_2$$. This is joint work with Ruibin Zhang and Kenji Iohara.