Mathematics Colloquia and Seminars

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Rational Cherednik algebras are a class of algebras associated to the action of a complex reflection group W on its reflection representation R. They depend on a parameter (to be thought of as a central character) and their representation theory is very similar to that of universal enveloping algebras. In particular, one can define a category O and Harish-Chandra bimodules. While the former has been studied intensively during recent years, many basic questions remain unknown about the latter category, e.g. the number of irreducible objects is unknown in general. In my talk, I will define these concepts, and present a description of the category of fully supported Harish-Chandra bimodules in terms of a certain normal subgroup of W that depends crucially on the parameter.