Rational Cherednik algebras and categorification

29 Sep 2015  ·  Losev Ivan ·

In this survey article we review Kac-Moody and Heisenberg algebra actions on the categories $\mathcal{O}$ of the rational Cherednik algebras associated to groups $G(\ell,1,n)$. Using these actions we solve basic representation theoretic problems for these categories such as the classification of finite dimensional irreducible representations and computation of characters of the irreducibles...

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Representation Theory