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Sur l’irréductibilité d’une induite parabolique


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Author: Mínguez Espallargas, Alberto
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2009
Published in: Journal für die reine und angewandte Mathematik, 629, 107-131.
Document type: Article
Abstract: Let F be a non-Archimedean locally compact field and let D be a central division algebra over F. Let p1 and p2 be respectively two smooth irreducible representations of GLðn1; DÞ and GLðn2; DÞ, n1; n2 f0. In this article, we give some su‰cient conditions on p1 and p2 so that the parabolically induced representation of p1 np2 to GLðn1 þ n2; DÞ has a unique irreducible quotient. In the case where p1 is a cuspidal representation, we compute the Zelevinsky’s parameters of such a quotient in terms of the parameters of p2. This is the key point for making explicit Howe correspondence for dual pairs of type II (cf. [A. Mínguez, Correspondance de Howe explicite : paires duales de type II, Ann. Ec. Norm. Sup., à paraître]).
Cite: Mínguez Espallargas, A. (2009). Sur l’irréductibilité d’une induite parabolique. Journal für die reine und angewandte Mathematik, 629, 107-131.
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DOI: 10.1515/CRELLE.2009.028

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