Tempered modules in exotic Deligne-Langlands correspondence
نویسنده
چکیده
The main purpose of this paper is to produce a geometric realization for the tempered modules of the affine Hecke algebra of type C (1) n with arbitrary, non-root of unity, unequal parameters, using the exotic DeligneLanglands correspondence ([Ka08a]). Our classification has several applications to the Weyl group module structure of the tempered Hecke algebra modules. In particular, we 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. This last combinatorial classification was expected from [HO97], and provides the L-solutions for the Lieb-McGuire system.
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