Harish-Chandra bimodules for rational Cherednik algebrasAlgebra & Discrete Mathematics
|Jose Simental Rodriguez, Northeastern University
|Mon, Oct 17 2016, 4:10PM
Associated to a pair of algebras quantizing the same graded, commutative Poisson algebra, we have a category of Harish-Chandra bimodules. These have been studied with some detail in the context of universal enveloping algebras, W-algebras and hypertoric enveloping algebras, among others. In this talk, I will introduce these concepts in the setting of rational Cherednik algebras. I will present the classification of irreducible HC bimodules for Cherednik algebras associated to the symmetric group, and the relation between the category O and that of HC bimodules. Time permitting, I will also sketch the classification of certain irreducible HC bimodules that works for any rational Cherednik algebra.