Ivan Losev
Published 2015-09-29Version 1
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.
Comments: 36 pages, survey
Blocks of category $\mathcal{O}$ for rational Cherednik algebras and of cyclotomic Hecke algebras of type G(r,p,n)
On isomorphisms of certain functors for Cherednik algebras
An algebraic approach to the KZ-functor for rational Cherednik algebras associated with cyclic groups
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