Representations of rational Cherednik algebras
  This paper surveys the representation theory of rational Cherednik algebras. We also discuss the representations of the spherical subalgebras. We describe in particular the results on category O. For type A, we explain relations with the Hilbert scheme of points on C^2. We insist on the analogy with the representation theory of complex semi-simple Lie algebras. 
Raphael Rouquier