Article
Sur l’irréductibilité d’une induite parabolique
Author/s | Mínguez Espallargas, Alberto |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2009 |
Deposit Date | 2016-10-17 |
Published in |
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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 p1 and p2 be respectively two smooth irreducible representations of GLðn1; DÞ and GLðn2; DÞ, n1; n2 f0. In this article, ... 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]). |
Funding agencies | Ministerio de Ciencia y Tecnología (MCYT). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) |
Project ID. | MTM2004-07203-C02-01 |
Citation | 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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