Rational Cherednik algebras and Hilbert schemes

Gordon, I. and Stafford, J.T. (2005) Rational Cherednik algebras and Hilbert schemes. Advances in Mathematics, 198, pp. 222-274. (doi: 10.1016/j.aim.2004.12.005)

Full text not currently available from Enlighten.

Abstract

Let Hc be the rational Cherednik algebra of type An-1 with spherical subalgebra Uc=eHce. Then Uc is filtered by order of differential operators, with associated graded ring View the MathML source where W is the nth symmetric group. We construct a filtered Z-algebra B such that, under mild conditions on c: • the category B-qgr of graded noetherian B-modules modulo torsion is equivalent to Uc-mod; • the associated graded Z-algebra View the MathML source has grB-lqgr≃coh Hilb(n), the category of coherent sheaves on the Hilbert scheme of points in the plane. This can be regarded as saying that Uc simultaneously gives a non-commutative deformation of h⊕h*/W and of its resolution of singularities Hilb(n)→h⊕h*/W. As we show elsewhere, this result is a powerful tool for studying the representation theory of Hc and its relationship to Hilb(n).

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:UNSPECIFIED
Authors: Gordon, I., and Stafford, J.T.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics

University Staff: Request a correction | Enlighten Editors: Update this record