An explicit computation of p-stabilized vectors
Journal de théorie des nombres de Bordeaux, Volume 26 (2014) no. 2, pp. 531-558.

In this paper, we give a concrete method to compute p-stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over p-adic fields. An application to the global setting is also discussed. In particular, we give an explicit p-stabilized form of a Saito-Kurokawa lift.

Nous donnons une méthode concrète pour calculer les vecteurs p-stables dans l’espace des éléments fixés par un sous-groupe parahorique d’un groupe réductif p-adique. Nous discutons d’une application globale et, en particulier, nous donnons un exemple explicite d’un relèvement de Saito-Kurokawa p-stable.

DOI: 10.5802/jtnb.878
Classification: 11F85, 22E50
Michitaka MIYAUCHI 1; Takuya YAMAUCHI 2

1 Faculty of Liberal Arts and Sciences Osaka Prefecture University 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, JAPAN
2 Department of mathematics, Faculty of Education Kagoshima University Korimoto 1-20-6 Kagoshima 890-0065, JAPAN and Department of mathematics University of Toronto Toronto, Ontario M5S 2E4, CANADA
     author = {Michitaka MIYAUCHI and Takuya YAMAUCHI},
     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},
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     language = {en},
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Michitaka MIYAUCHI; Takuya YAMAUCHI. An explicit computation of $p$-stabilized vectors. Journal de théorie des nombres de Bordeaux, Volume 26 (2014) no. 2, pp. 531-558. doi : 10.5802/jtnb.878.

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