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arXiv · 1709.02989

Elliptic Double Affine Hecke Algebras

Eric M. Rains
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Abstract

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.

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Eric M. Rains. 2017-09-09. Elliptic Double Affine Hecke Algebras. https://doi.org/10.3842/sigma.2020.111

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