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κ-types and Γ-asymptotic expansions
-
Ju-Lee Kim
and
Fiona Murnaghan
Published/Copyright:
May 4, 2006
Abstract
Let G be the k-rational points of a connected reductive k-group, where k is a p-adic field of characteristic zero. We define a notion of strongly good positive G-datum Σ, and construct a κ-type associated to such a datum, following the methods of Yu's construction of types. Suppose π is an irreducible admissible representation of G of positive depth, containing such a κ-type. Then assuming that the residual characteristic of k is sufficiently large, we prove that the character of π is Γ-asymptotic on a G-domain defined in terms of Σ, where Γ is a semisimple element naturally associated to Σ. We also obtain a domain of validity for the Shalika germ expansion around the element Γ.
Received: 2004-01-21
Revised: 2005-05-27
Published Online: 2006-05-04
Published in Print: 2006-03-24
© Walter de Gruyter
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Articles in the same Issue
- Lines on projective hypersurfaces
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- On the growth rate of the tunnel number of knots
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- Exponential product approximation to the integral kernel of the Schrödinger semigroup and to the heat kernel of the Dirichlet Laplacian
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