Normalisation des opérateurs d'entrelacement et réductibilité des induites de cuspidales; le cas des groupes classiques $p$-adiques. (Normalization of intertwining operators and reducibility of representations induced from cuspidal ones; the case of $p$-adic classical groups)

C. Moeglin

Review from Zentralblatt MATH:

Let $G(n)$ denote a symplectic or an orthogonal group of rank $n$ over a non-archimedean local field $F$. Let $\pi$ be an irreducible cuspidal representation of $G(n,F)$ and $\rho$ an irreducible unitary cuspidal representation of $\text{GL} (c,F)$. Then $\text{GL} (c)\times G(n)$ is imbedded in $G(n+c)$ as a Levi group of a maximal parabolic subgroup and we have the induced representation $I(\rho,\pi,s) = \rho |\text{det}|^s \times \pi$ of $\text{GL} (n+c,F)$. The subject of the article is the determination of the values of $s$ for which this representation is reducible and the normalization of the intertwining operators from $I(\rho,\pi,s)$ to $I(\rho^{\ast},\pi,-s)$. A normalization is given under the assumption that $\pi$ comes from a global representation which satisfies a certain functoriality condition with respect to a general linear group.

Reviewed by J.G.M.Mars

Classification (MSC2000): 22E50

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