Tempered modules in exotic Deligne-Langlands correspondence

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Abstract

We present a geometric description for tempered modules of the affine Hecke algebra of type Cnwith arbitrary (non-root of unity) unequal parameters, using the exotic Deligne-Langlands correspondence (Kato (2009) [18]). Our description has several applications to the structure of the tempered 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 latter combinatorial classification was expected from Heckman and Opdam (1997) [15], and determines the L2-solutions for the Lieb-McGuire system. © 2010 Elsevier Inc.

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Ciubotaru, D., & Kato, S. (2011). Tempered modules in exotic Deligne-Langlands correspondence. Advances in Mathematics, 226(2), 1538–1590. https://doi.org/10.1016/j.aim.2010.08.013

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