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

Takeshi Suzuki·Monica Vazirani
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Abstract

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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Takeshi Suzuki, Monica Vazirani. 2005-08-08. Tableaux on periodic skew diagrams and irreducible representations of the double affine Hecke algebra of type A. https://arxiv.org/abs/math/0406617

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