A remark on rational Cherednik algebras and differential operators on the cyclic quiver

Details A remark on rational Cherednik algebras and differential operators on the cyclic quiver A remark on rational Cherednik algebras and differential operators on the cyclic quiver

2005-07-20

arxiv.org/abs/math/0507413v1

Mathematics

Representation Theory

Scientific paper

We show that the spherical subalgebra of the rational Cherednik algebra associated to the wreath product of a symmetric group and a cyclic group is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver. This confirms a version of a conjecture of Etingof and Ginzburg in the case of cyclic groups. The proof is a straightforward application of work of Oblomkov on the deformed Harish-Chandra homomorphism, and of Crawley-Boevey and of Gan and Ginzburg on preprojective algebras.

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