Affine Lie algebras and rational Cherednik algebras via the Suzuki functor

The Suzuki functor connects the representation theory of the affine Lie algebra to the representation theory of the rational Cherednik algebra in type A. In this talk we generalize Suzuki's original construction to the critical level case. One of the main reasons why the critical level is special is the fact that the corresponding category of smooth modules has a large centre. We study how the Suzuki functor relates it to the centre of the rational Cherednik algebra at t=0. We also interpret our results geometrically, linking the Calogero-Moser space with opers on the punctured disc.