Tempered modules in exotic Deligne-Langlands correspondence

Abstract

The main purpose of this paper is to identify the tempered modules for the affine Hecke algebra of type $C_n^{(1)}$ with arbitrary, non-root of unity, unequal parameters, in the exotic Deligne-Langlands correspondence in the sense of Kato. 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 sign representation of the Weyl group. This last combinatorial classification was expected from the work of Heckman-Opdam and Slooten.

51 pages

References in corpus (1)

• Discrete series characters for affine Hecke algebras and their formal degrees

Cited by in corpus (2)

• On the classification of irreducible representations of affine Hecke algebras with unequal parameters
• Spin representations of Weyl groups and the Springer correspondence