  In the previous author's paper the Macdonald norm conjecture (including the
famous constant term conjecture) was proved. This paper contains the proof of
the remaining two (the duality and evaluation conjectures). The evaluation
theorem is in fact a $q,t$-generalization of the classic Weyl dimension
formula. As to the duality theorem, it states that the generalized
trigonometric-difference zonal Fourier transform is self-dual (at least
formally). We define this transform in terms of double affine Hecke algebras
related to elliptic braid groups. The duality appeared to be directly connected
with the transposition of the periods of an elliptic curve.
