Sur l'irréductibilité d'une induite parabolique
| dc.creator | Minguez, Alberto | |
| dc.date | 2007-09-20 | |
| dc.date.accessioned | 2026-07-07T08:31:04Z | |
| dc.date.available | 2026-07-07T08:31:04Z | |
| dc.description | Let $F$ 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.identifier | https://arxiv.org/abs/0709.3194 | |
| dc.identifier | http://arxiv.org/abs/0709.3194 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138404 | |
| dc.subject | Representation Theory | |
| dc.subject | 22E50, 22E35 | |
| dc.title | Sur l'irréductibilité d'une induite parabolique | |
| dc.type | text |