We introduce the generic central character of an irreducible discrete series representation of an affine Hecke algebra. Using this invariant we give a new classification of the irreducible discrete series characters for all abstract affine Hecke algebras (except for the types ${E_{n}^{(1)}}$ , n=6,
In this paper we study homological properties of modules over an affine Hecke algebra H. In particular we prove a comparison result for higher extensions of tempered modules when passing to the Schwartz algebra S, a certain topological completion of the affine Hecke algebra. The proof is self-contai
This paper is a further development of complex methods in harmonic analysis on semi-simple Lie groups [AG], [BeR], [KrS1,2]. We study the growth behaviour of the holomorphic extension of the orbit map of the spherical vector of an irreducible spherical representation of a real reductive group G when
Abstract: We give conceptual proofs of certain basic properties of the arrangement of shifted root hyperplanes associated to a root system R0 and a W0=W(R0)-invariant real valued parameter function on R0. The method is based on the role of this shifted root hyperplane arrangement for the harmonic an
Abstract In this paper we study root system generalizations of the quantum Bose-gas on the circle with pair-wise delta-function interactions. The underlying symmetry structures are shown to be governed by the associated graded algebra of Cherednik's (suitably filtered) degenerate double affine Hecke
Abstract: An affine Hecke algebra H contains a large abelian subalgebra A spanned by the Bernstein-Zelevinski-Lusztig basis elements theta x, where x runs over (an extension of) the root lattice. The centre Z of H is the subalgebra of Weyl group invariant elements in A. The natural trace ('evaluatio
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