Representations of rational Cherednik algebras

Conference item

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.

Authors: Rouquier, R

• Journal: CONTEMP MATH
• Volume: 392
• Pages: 103-131
• Publication date: 2005-01-01
• Event title: International Conference on Infinite-Dimensional Aspects of Representation Theory and Applications
• Keywords: INVARIANTS; QUOTIENT SINGULARITIES; affine hecke algebras; DUNKL OPERATORS; DEFORMATIONS; MONODROMY REPRESENTATIONS; DIFFERENTIAL-DIFFERENCE OPERATORS; KNIZHNIK-ZAMOLODCHIKOV EQUATIONS; CATEGORY-O; SYMPLECTIC REFLECTION ALGEBRAS