La formule des traces pour les revêtements de groupes réductifs connexes. II. Analyse harmonique locale  [ The trace formula for coverings of connected reductive groups. II. Local harmonic analysis ]
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 5, p. 787-859

We establish some results in local harmonic analysis which are necessary for Arthur's invariant trace formula for coverings of connected reductive groups. More precisely, for local coverings we will study (1) the Plancherel formula and its preparations, (2) the normalization of intertwining operators subject to Arthur's conditions, (3) the local behavior of characters of admissible representations in the nonarchimedean case, and (4) the genuine part of the invariant local trace formula. As a byproduct of the invariant local trace formula, we deduce the density of tempered characters for coverings.

On établit des résultats de l'analyse harmonique locale nécessaires pour la formule des traces invariante d'Arthur pour les revêtements de groupes réductifs connexes. Plus précisément, on démontre pour les revêtements locaux (1) la formule de Plancherel et des préparatifs reliés, (2) la normalisation des opérateurs d'entrelacement soumise aux conditions d'Arthur, (3) le comportement local de caractères de représentations admissibles dans le cas non archimédien, et (4) la partie spécifique de la formule des traces locale invariante. Comme un sous-produit de la démonstration de la formule des traces locale invariante, on obtient aussi la densité de caractères tempérés pour les revêtements.

DOI : https://doi.org/10.24033/asens.2178
Classification:  11F72,  11F70
Keywords: Arthur-Selberg trace formula, local trace formula, covering groups
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     author = {Li, Wen-Wei},
     title = {La formule des traces pour les rev\^etements de groupes r\'eductifs connexes. II. Analyse harmonique locale},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {4e s{\'e}rie, 45},
     number = {5},
     year = {2012},
     pages = {787-859},
     doi = {10.24033/asens.2178},
     mrnumber = {3053009},
     language = {fr},
     url = {http://www.numdam.org/item/ASENS_2012_4_45_5_787_0}
}
Li, Wen-Wei. La formule des traces pour les revêtements de groupes réductifs connexes. II. Analyse harmonique locale. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 5, pp. 787-859. doi : 10.24033/asens.2178. http://www.numdam.org/item/ASENS_2012_4_45_5_787_0/

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