• Corpus ID: 14396490

# Hilbert schemes, Hecke algebras and the Calogero-Sutherland system

```@article{Costello2003HilbertSH,
title={Hilbert schemes, Hecke algebras and the Calogero-Sutherland system},
author={Kevin J. Costello and Ian Grojnowski},
journal={arXiv: Algebraic Geometry},
year={2003}
}```
• Published 13 October 2003
• Mathematics
• arXiv: Algebraic Geometry
We describe the ring structure of the cohomology of the Hilbert scheme of points for a smooth surface X. When X is C 2 , this was done in [13, 21] by realising this ring as a degeneration of the center of CSn. When the canonical class KX = 0, [14] extended this result by defining an algebra structure on H � ({(x, g) ∈ X n × Sn | gx = x}); the Sn-invariants of this algebra is the desired ring. But when KX 6 0 it seems no such algebra can exist. A completely different approach is needed. Instead…
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The purpose of this paper is to throw a bridge between two seemingly unrelated subjects. One is the Hilbert scheme of points on projective surfaces, which has been intensively studied by various
This is the first in a series of papers which describe the action of an affine Lie algebra with central charge \$n\$ on the moduli space of \$U(n)\$-instantons on a four manifold \$X\$. This generalises
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We develop representation theory of the rational Cherednik algebra H associated to a finite Coxeter group W in a vector space h. It is applied to show that, for integral values of parameter `c', the
Several authors have been interested in the Hilbert scheme SPq:=Hilb"(S) parametrizing finite subschemes of length n on a smooth projective surface S. In EF 1] and I-F 2] Fogarty shows that S tnj is
• Mathematics
• 2001
We construct geometrically the generating fields of a W algebra which acts irreducibly on the direct sum of the cohomology rings of the Hilbert schemes of n points on a projective surface for all n.
Abstract. We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on a smooth surface within the framework of
This paper is the course of lectures delivered by the first author in Kyoto in 1996-97 and recorded by the others. We tried to follow closely the notes of the lectures not yielding to the temptation
We give a reinterpretation of the matrix theory discussed by Moore, Nekrasov and Shatashivili (MNS) in terms of the second quantized operators which describes the homology class of the Hilbert scheme
• Mathematics
• 2000
To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A^[n] in such a way that for any smooth projective surface X with trivial canonical divisor there is a canonical
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• 2000
Let C(Sn) be the Z-module of integer valued class functions on the symmetric group Sn. We introduce a graded version of the con- volution product on C(Sn) and show that there is a degree preserving