  We introduce and study an affine analogue of skew Young diagrams and tableaux
on them.
  It turns out that the double affine Hecke algebra of type $A$ acts on the
space spanned by standard tableaux on each diagram. It is shown that the
modules obtained this way are irreducible, and they exhaust all irreducible
modules of a certain class over the double affine Hecke algebra. In particular,
the classification of irreducible modules of this class, announced by
Cherednik, is recovered.
