Elliptic Double Affine Hecke Algebras
Algebraic Geometry
2020-11-06 v3 Quantum Algebra
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 version of the construction to construct a flat noncommutative deformation of the 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.
Cite
@article{arxiv.1709.02989,
title = {Elliptic Double Affine Hecke Algebras},
author = {Eric M. Rains},
journal= {arXiv preprint arXiv:1709.02989},
year = {2020}
}