Elliptic Double Affine Hecke Algebras

Symmetry Integrability and Geometry-Methods and Applications

article

Eric M. Rains¹ 

[1] Department of Mathematics, California Institute of Technology

关键词: elliptic curves;    Hecke algebras;    noncommutative deformations 2020 Mathematics Subject Classification 33D80;    39A70;    14A22;   

DOI  :  10.3842/SIGMA.2020.111

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown