Geodesic
Elliptic Double Affine Hecke Algebras
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra. As an application, we use a variant of the $\tilde{C}_n$ version of the construction to construct a flat noncommutative deformation of the $n$th symmetric power of any rational surface with a smooth anticanonical curve, and give a further construction which conjecturally is a corresponding deformation of the Hilbert scheme of points.
Keywords: elliptic curves, Hecke algebras, noncommutative deformations. 
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     author = {Eric M. Rains},
     title = {Elliptic {Double} {Affine} {Hecke} {Algebras}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a110/}
}
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Eric M. Rains. Elliptic Double Affine Hecke Algebras. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a110/

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