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.