Let $H\_{n}$ be the affine Hecke algebra with parameter q, where q is not root of unity.  

The classification of irreducible finite dimensional representations has been given by Kazhdan-Lusztig in terms of geometric data.. I wonder in the case of type A, is there any classification in terms of concrete combinatoric?


The reason I ask this question is that, for degenerate affine Hecke algebra in type A, all finite dimensional represetnations can be parametrized by two sequences of complex numbers,
$\lambda=(\lambda\_1,\lambda\_2,\cdots,\lambda\_n) $, $\mu=(\mu\_1,\mu\_2,\cdots,\mu\_n) $, such that , $\lambda$ abnd $\mu$ satifisy some simple combinatorics conditions.


It is well known that affine hecke algebra is closely related to degenerate affine Hecke algebra.


I hope and expect there should be similar even the same classifciation in the case type A.



classification of irreducible finite dimensional representation of affine hecke algebra of type A
This is done in Orellana-Ram, `[Affine braids, Markov Traces and the category O](http://arxiv.org/abs/math/0401317)'. The answer is essentially the same as for the degenerate affine Hecke algebra.


