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Normalisation des op\'erateurs d'entrelacement et r\'eductibilit\'e des induites de cuspidales; le cas des groupes classiques p-adiques

Colette Mœglin
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Abstract

On montre comment les conjectures d'Arthur permettent de calculer les points de r\'eductibilit\'e pour les induites de cuspidales des groupes classiques. Les conjectures d'Arthur utilis\'ees portent sur l'existence d'un rel\`evement faible des repr\'esentations automorphes cuspidales d'un groupe classique vers un groupe lin\'eaire convenable. Et les points de r\'eductibilit\'es sont decrits en terme de la g\'eom\'etrie des orbites unipotentes des groupe dual. On en d\'eduit des r\'esultats sur la normalisation des operateurs d'entrelacement. We show how the global conjectures of Arthur allow us to calculate the points of irreducibility for representations induced from cuspidal representations of classical groups. The conjectures of Arthur used are concerned with the existence of weak liftings of automorphic representations from classical groups to suitable linear ones. And the points of irreducibility are described in terms of the geometry of unipotent orbits on the dual group. We deduce certain results about the normalization of intertwining operators.

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Colette Mœglin. 2000-03-01. Normalisation des op\'erateurs d'entrelacement et r\'eductibilit\'e des induites de cuspidales; le cas des groupes classiques p-adiques. https://arxiv.org/abs/math/0003242

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