A Remark on Rational Cherednik Algebras and Differential Operators on the Cyclic Quiver
نویسنده
چکیده
We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn o C`, the wreath product of the symmetric group and the cyclic group of order `, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size `. This confirms a version of [EG, Conjecture 11.22] in the case of cyclic groups. The proof is a straightforward application of work of Oblomkov, [O], on the deformed Harish–Chandra homomorphism, and of Crawley–Boevey, [CB1] and [CB2], and Gan and Ginzburg, [GG], on preprojective algebras.
منابع مشابه
A Remark on Rational Cherednik Algebras and Differential Operators on the Cyclic Quiver
We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn ≀ Cl, the wreath product of the symmetric group and the cyclic group of order l, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size l. This confirms a version of [EG, Conjecture 11.22] in the case of cyclic groups. The ...
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