scholarly journals Induced and simple modules of double affine Hecke algebras

2005 ◽  
Vol 126 (2) ◽  
pp. 251-323 ◽  
Author(s):  
Eric Vasserot
Keyword(s):  
Hecke Algebras ◽  
Simple Modules ◽  
Double Affine Hecke Algebras ◽  
Affine Hecke Algebras

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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