## Normalization of intertwining operators and reducibility of representations induced from cuspidal ones; the case of $$p$$-adic classical groups. (Normalisation des opérateurs d’entrelacement et réductibilité des induites de cuspidales; le cas des groupes classiques $$p$$-adiques.)(French)Zbl 0956.22012

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.

### MSC:

 2.2e+51 Representations of Lie and linear algebraic groups over local fields
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