For affine Hecke algebra, generically the classification of irreducible modules is given by DeligneLanglands 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 DeligneLanglands 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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