Explicit functorial correspondences for level zero representations of p-adic linear groups

JOURNAL OF NUMBER THEORY

卷:131

Article

Bushnell, Colin J.¹  Henniart, Guy^2,3 

[1] Kings Coll London, Dept Math, London WC2R 2LS, England

[2] Univ Paris 11, Lab Math Orsay, F-91405 Orsay, France

[3] CNRS, F-91405 Orsay, France

关键词: Explicit local Langlands correspondence;    Jacquet-Langlands correspondence;    Extended simple type;    Tame admissible pair;    Level zero representation;    Weil-Deligne representation;   

DOI  :  10.1016/j.jnt.2010.09.003

来源: Elsevier

【 摘 要 】

Let F be a non-Archimedean local field and D a central F-division algebra of dimension n(2), n >= 1. We consider first the irreducible smooth representations of D-x trivial on 1-units, and second the indecomposable, n-dimensional, semisimple, Weil-Deligne representations of F which are trivial on wild inertia. The sets of equivalence classes of these two sorts of representations are in canonical (functorial) bijection via the composition of the Jacquet-Langlands correspondence and the Langlands correspondence. They are also in canonical bijection via explicit parametrizations in terms of tame admissible pairs. This paper gives the relation between these two bijections. It is based on analysis of the discrete series of the general linear group GL(n)(F) in terms of a classification by extended simple types. (C) 2010 Elsevier Inc. All rights reserved.

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