[Representations and quasi-characters of level ; endoscopy]
Let be a finite extension of and let be a connected reductive group over . We assume that is large relatively to . Let be an endoscopic group of . Following Arthur, we have, roughly speaking, a spectral transfer morphism, denoted by , which, to a stable finite linear combination of irreducible admissible representations of , associates a finite linear combination of irreducible admissible representations of . Let be the Bernstein’s projector such that, for an irreducible admissible representation of , we have if has level and if has strictly positive level. Define similarly . We prove that preserves the space of stable finite linear combinations of irreducible admissible representations of and that .
Soient une extension finie de et un groupe réductif connexe défini sur . On suppose que est grand relativement à . Soit un groupe endoscopique de . D’après Arthur, il existe un homomorphisme de transfert spectral. Grosso modo, à une combinaison linéaire stable de représentations admissibles et irréductibles de , il associe une combinaison linéaire de représentations admissibles et irréductibles de . On note cet homomorphisme. Notons le projecteur de Bernstein tel que, pour une représentation admissible et irréductible de , on a si est de niveau et si est de niveau strictement positif. On définit de même . On démontre que préserve l’espace des combinaisons linéaires stables de représentations admissibles et irréductibles de et que .
Accepted:
Published online:
Mot clés : Représentations de niveau $0$, transfert endoscopique
Keywords: Representations of depth $0$, endoscopic transfer
Jean-Loup Waldspurger 1
@article{JEP_2021__8__193_0, author = {Jean-Loup Waldspurger}, title = {Repr\'esentations et quasi-caract\`eres de~niveau~$0$~; endoscopie}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {193--278}, publisher = {\'Ecole polytechnique}, volume = {8}, year = {2021}, doi = {10.5802/jep.145}, language = {fr}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.145/} }
TY - JOUR AU - Jean-Loup Waldspurger TI - Représentations et quasi-caractères de niveau $0$ ; endoscopie JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 193 EP - 278 VL - 8 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.145/ DO - 10.5802/jep.145 LA - fr ID - JEP_2021__8__193_0 ER -
%0 Journal Article %A Jean-Loup Waldspurger %T Représentations et quasi-caractères de niveau $0$ ; endoscopie %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 193-278 %V 8 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.145/ %R 10.5802/jep.145 %G fr %F JEP_2021__8__193_0
Jean-Loup Waldspurger. Représentations et quasi-caractères de niveau $0$ ; endoscopie. Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 193-278. doi : 10.5802/jep.145. https://jep.centre-mersenne.org/articles/10.5802/jep.145/
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