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Harish-Chandra bimodules for rational Cherednik algebras

Algebra & Discrete Mathematics

Speaker: Jose Simental Rodriguez, Northeastern University
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Location: 1147 MSB
Start time: 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.