A question on the representations of affine Hecke algebras In the paper Proof of the Deligne-Langlands conjecture for Hecke algebras, Kazhdan and Lusztig give a classification of simple modules of the affine Hecke algebra associated to a connected reductive linear group with simply connected derived subgroup (requiring that the parameter $q$ is not a root of unity).
I wonder whether we have a classification of simple modules for affine Hecke algebras associated to general reductive linear groups without the restriction of simply connectedness.
 A: This is perhaps overkill for your question, but there is a classification for the simple modules of an interesting family of affine Hecke algebras even with (certain) unequal parameters due to Lusztig. The proof is different from the one in the original case by Kazhdan and Lusztig, using equivariant perverse sheaves and the graded affine Hecke algebra. The first paper associates to an affine Hecke algebra (attached to any root datum) a graded version, and shows how the classification of simple modules (when $q$ is not a root of unity) can be reduced to the same classification problem for the graded algebras (though for a single affine Hecke algebra, one needs to understand the irreducibles for possibly smaller graded Hecke algebras, as well as the irreducibles for it own associated graded Hecke algebra).
The problem of classifying simple modules for the graded algebras (with a certain family of parameters arising from the study of unipotent representations of $p$-adic groups) is then taken up in a series of papers Lusztig wrote on "Cuspidal local systems" which solves the problem by geometric means (perverse sheaves and equivariant cohomology). This is then used in two later papers to give a complete "Langlands style" classification of the unipotent representations of simple $p$-adic groups.
