scholarly journals Generalized double affine Hecke algebras of higher rank

2006 ◽  
Vol 2006 (600) ◽  
Author(s):  
Pavel Etingof ◽  
Wee Liang Gan ◽  
Alexei Oblomkov
Keyword(s):  
Hecke Algebras ◽  
Double Affine Hecke Algebras ◽  
Affine Hecke Algebras ◽  
Higher Rank

scholarly journals Cyclotomic double affine Hecke algebras and affine parabolic category O

2010 ◽  
Vol 225 (3) ◽  
pp. 1523-1588 ◽  
Author(s):  
M. Varagnolo ◽  
E. Vasserot
Keyword(s):  
Hecke Algebras ◽  
Double Affine Hecke Algebras ◽  
Affine Hecke Algebras

scholarly journals Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces

2007 ◽  
Vol 212 (2) ◽  
pp. 749-796 ◽  
Author(s):  
Pavel Etingof ◽  
Alexei Oblomkov ◽  
Eric Rains
Keyword(s):  
Hecke Algebras ◽  
Del Pezzo Surfaces ◽  
Double Affine Hecke Algebras ◽  
Affine Hecke Algebras ◽  
Del Pezzo

scholarly journals The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials

2010 ◽  
Vol 147 (1) ◽  
pp. 188-234 ◽  
Author(s):  
O. Schiffmann ◽  
E. Vasserot
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Moduli Space ◽  
Vector Bundles ◽  
Hecke Algebras ◽  
Macdonald Polynomials ◽  
Hall Algebra ◽  
Double Affine Hecke Algebras ◽  
Affine Hecke Algebras ◽  
Semistable Vector Bundles

AbstractWe exhibit a strong link between the Hall algebra HX of an elliptic curve X defined over a finite field 𝔽l (or, more precisely, its spherical subalgebra U+X) and Cherednik’s double affine Hecke algebras $\ddot {\mathbf {H}}_n$ of type GLn, for all n. This allows us to obtain a geometric construction of the Macdonald polynomials Pλ(q,t−1) in terms of certain functions (Eisenstein series) on the moduli space of semistable vector bundles on the elliptic curve X.

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