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For affine Hecke algebra, generically the classification of irreducible modules is given by Deligne-Langlands conjecture. It seems that the corresponding classification problem for degenerate affine Hecke algebra is easier. I don't know how, but it is my feeling. Let q be the parameter, if q is a root of unity, as I understand Deligne-Langlands conjecture doesn't hold in general. In this case is there still any classification theorem? For degenerate affine Hecke algebra, where can I find the reference for classification? In type A, if i understand correctly, it is more or less clear since we have categorification of half of enveloping algebra of certain Kac moody algebra.

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There are two recent papers by Varagnolo and Vasserot dealing with the affine Hecke algebras of type B and D (arXiv:0911.5209 and 0912.4245, respectively). These are some sort of categorification result (I haven't had a chance to read them yet). – David Hill May 16 '11 at 23:20

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