Tableaux on periodic skew diagrams and irreducible representations of   the double affine Hecke algebra of type A
  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. 
Takeshi Suzuki, Monica Vazirani