39 research outputs found
Extensions of tempered representations
Let be irreducible tempered representations of an affine Hecke
algebra H with positive parameters. We compute the higher extension groups
explicitly in terms of the representations of analytic
R-groups corresponding to and . The result has immediate
applications to the computation of the Euler-Poincar\'e pairing ,
the alternating sum of the dimensions of the Ext-groups. The resulting formula
for is equal to Arthur's formula for the elliptic pairing of
tempered characters in the setting of reductive p-adic groups. Our proof
applies equally well to affine Hecke algebras and to reductive groups over
non-archimedean local fields of arbitrary characteristic. This sheds new light
on the formula of Arthur and gives a new proof of Kazhdan's orthogonality
conjecture for the Euler-Poincar\'e pairing of admissible characters.Comment: This paper grew out of "A formula of Arthur and affine Hecke
algebras" (arXiv:1011.0679). In the second version some minor points were
improve
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On Completions of Hecke Algebras
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