Tempered modules in exotic Deligne-Langlands correspondence (Q616893)

The authors present a geometric description for tempered modules of the affine Hecke algebra of type \(C_n\) with arbitrary (non-root of unity) unequal parameters, using the exotic Deligne-Langlands correspondence. This has several applications to the structure of the tempered modules. In particular, they provide a geometric and a combinatorial classification of discrete series which contain the sgn representation of the Weyl group, equivalently, via the Iwahori-Matsumoto involution, of spherical cuspidal modules.