scholarly journals The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case

2007 ◽  
Author(s):  
Tom H. Koornwinder
Keyword(s):  
Hecke Algebra ◽  
Affine Hecke Algebra ◽  
Double Affine Hecke Algebra ◽  
Rank One ◽  
The Relationship

scholarly journals Elliptic Double Affine Hecke Algebras

2020 ◽  
Author(s):  
Eric M. Rains ◽  
Keyword(s):  
Hilbert Scheme ◽  
Hecke Algebra ◽  
Rational Surface ◽  
Symmetric Power ◽  
Affine Hecke Algebra ◽  
Double Affine Hecke Algebra ◽  
Affine Weyl Group ◽  
Double Affine Hecke Algebras ◽  
Hilbert Scheme Of Points ◽  
Affine Hecke Algebras

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<sub>n</sub> version of the construction to construct a flat noncommutative deformation of the nth 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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