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)
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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 |
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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 |
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