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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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1435-5345
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Sur l'irréductibilité d'une induite parabolique

Alberto Mínguez
  • Laboratoire de Mathématiques, Université Paris-Sud, Bât. 425, 91405 Orsay Cedex, France, CNRS UMR 8628. e-mail:
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Abstract

Let F be a non-Archimedean locally compact field and let D be a central division algebra over F. Let π1 and π2 be respectively two smooth irreducible representations of GL(n 1, D) and GL(n 2, D), n 1, n 2 ≧ 0. In this article, we give some sufficient conditions on π1 and π2 so that the parabolically induced representation of π1 ⊗ π2 to GL(n 1 + n 2, D) has a unique irreducible quotient. In the case where π1 is a cuspidal representation, we compute the Zelevinsky's parameters of such a quotient in terms of the parameters of π2. This is the key point for making explicit Howe correspondence for dual pairs of type II (cf. [Mínguez, thesis, Orsay 2006]).

About the article

Received: 2007-05-11

Revised: 2008-02-04


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Pages -–-, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2009.028.

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[1]
Shunsuke Yamana
Pacific Journal of Mathematics, 2013, Volume 264, Number 1, Page 235

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