The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials

We exhibit a strong link between the Hall algebra H(X) of an elliptic curve X defined over a finite field F(l) (or, more precisely, its spherical subalgebra U(X)(+)) and Cherednik's double affine Hecke algebras (H) double over dot(n) of type GL(n) for all n. This allows us to obtain a geometric construction of the Macdonald polynomials P(lambda)(q, t(-1)) in terms of certain functions (Eisenstein series) on the moduli space of semistable vector bundles on the elliptic curve X.