English

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 C~n\tilde{C}_n version of the construction to construct a flat noncommutative deformation of the nnth 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

Cite

@article{arxiv.1709.02989,
  title  = {Elliptic Double Affine Hecke Algebras},
  author = {Eric M. Rains},
  journal= {arXiv preprint arXiv:1709.02989},
  year   = {2020}
}
R2 v1 2026-06-22T21:38:00.082Z