Nous donnons une méthode concrète pour calculer les vecteurs -stables dans l’espace des éléments fixés par un sous-groupe parahorique d’un groupe réductif -adique. Nous discutons d’une application globale et, en particulier, nous donnons un exemple explicite d’un relèvement de Saito-Kurokawa -stable.
In this paper, we give a concrete method to compute -stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over -adic fields. An application to the global setting is also discussed. In particular, we give an explicit -stabilized form of a Saito-Kurokawa lift.
@article{JTNB_2014__26_2_531_0,
author = {MIYAUCHI, Michitaka and YAMAUCHI, Takuya},
title = {An explicit computation of $p$-stabilized vectors},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {531--558},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {26},
number = {2},
year = {2014},
doi = {10.5802/jtnb.878},
mrnumber = {3320491},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.878/}
}
TY - JOUR AU - MIYAUCHI, Michitaka AU - YAMAUCHI, Takuya TI - An explicit computation of $p$-stabilized vectors JO - Journal de théorie des nombres de Bordeaux PY - 2014 SP - 531 EP - 558 VL - 26 IS - 2 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.878/ DO - 10.5802/jtnb.878 LA - en ID - JTNB_2014__26_2_531_0 ER -
%0 Journal Article %A MIYAUCHI, Michitaka %A YAMAUCHI, Takuya %T An explicit computation of $p$-stabilized vectors %J Journal de théorie des nombres de Bordeaux %D 2014 %P 531-558 %V 26 %N 2 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.878/ %R 10.5802/jtnb.878 %G en %F JTNB_2014__26_2_531_0
MIYAUCHI, Michitaka; YAMAUCHI, Takuya. An explicit computation of $p$-stabilized vectors. Journal de théorie des nombres de Bordeaux, Tome 26 (2014) no. 2, pp. 531-558. doi : 10.5802/jtnb.878. http://www.numdam.org/articles/10.5802/jtnb.878/
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