Tableaux on periodic skew diagrams and irreducible representations of the double affine Hecke algebra of type A

Details Tableaux on periodic skew diagrams and irreducible representations of the double affine Hecke algebra of type A Tableaux on periodic skew diagrams and irreducible representations of the double affine Hecke algebra of type A

2004-06-30

arxiv.org/abs/math/0406617v2

Mathematics

Quantum Algebra

34 pages. In ver.2, the title is changed and some typos are corrected

Scientific paper

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.

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