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

Research output: Contribution to journalArticlepeer-review

Colin J. Bushnell, Guy Henniart

Original languageEnglish
Pages (from-to)309 - 331
Number of pages23
JournalJournal of Number Theory
Issue number2
PublishedFeb 2011

King's Authors


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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