  We show that the Hall algebra of the category of coherent sheaves on an
elliptic curve (or, equivalently, the algebra of unramified automorphic forms
for GL(n) for all n) is equal to the stable limit of spherical double affine
Hecke algebras for GL(k) as k goes to infinity. The two parameters correspond
to the size of the finite field and the modulus of the elliptc curve. Under
this isomorphism the Hecke operators are mapped to the Macdonald operators.
This allows us to give a geometric construction of Macdonald polynomials
(eigenvectors for the Macdonald operator) in terms of a suitable specialization
of Eisenstein series (eigenvectors for the Hecke operators).
