Ju-Lee Kim, Fiona Murnaghan
&kgr;-types and Γ-asymptotic expansions
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 &kgr;-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 &kgr;-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.
Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter
Print ISSN: 0075-4102
Volume: 2006, 03/2006
Pages: 189 - 236
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