Sur l'irréductibilité d'une induite parabolique

dc.creatorMinguez, Alberto
dc.date2007-09-20
dc.date.accessioned2026-07-07T08:31:04Z
dc.date.available2026-07-07T08:31:04Z
dc.descriptionLet $F$ be a non-Archimedean locally compact field and let $D$ be a central division algebra over $F$. Let $π_1$ and $π_2$ be respectively two smooth irreducible representations of ${\rm GL}(n_1,D)$ and ${\rm GL}(n_2,F)$, $n_1, n_2 \geq 0$. In this article, we give some sufficient conditions on $π_1$ and $π_2$ so that the parabolically induced representation of $π_1 \otimes π_2$ to ${\rm GL}(n_1+n_2,D)$ has a unique irreducible quotient. In the case where $π_1$ is a cuspidal representation, we compute the Zelevinsky's parameters of such a quotient in terms of parameters of $π_2$. This is the key point for making explicit Howe correspondence for dual pairs of type II.
dc.identifierhttps://arxiv.org/abs/0709.3194
dc.identifierhttp://arxiv.org/abs/0709.3194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138404
dc.subjectRepresentation Theory
dc.subject22E50, 22E35
dc.titleSur l'irréductibilité d'une induite parabolique
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