In this paper we explicitly determine the Macdonald formula for spherical functions on any locally finite, regular and affine Bruhat-Tits building, by constructing the finite difference equations that must be satisfied and explaining how they arise, by only using the geometric properties of the building.
On détermine explicitement la formule de Macdonald pour les fonctions sphériques sur tout immeuble de Bruhat-Tits localement fini, régulier et affine en construisant d’une manière motivée les équations aux différences finies qu’elles doivent satisfaire, n’utilisant que les propriétés géométriques de l’immeuble.
@article{AFST_2011_6_20_4_669_0,
author = {A. M. Mantero and A. Zappa},
title = {Macdonald formula for spherical functions on affine buildings},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {669--758},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 20},
number = {4},
year = {2011},
doi = {10.5802/afst.1321},
mrnumber = {2918211},
zbl = {1247.43012},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1321/}
}
TY - JOUR AU - A. M. Mantero AU - A. Zappa TI - Macdonald formula for spherical functions on affine buildings JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2011 SP - 669 EP - 758 VL - 20 IS - 4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1321/ DO - 10.5802/afst.1321 LA - en ID - AFST_2011_6_20_4_669_0 ER -
%0 Journal Article %A A. M. Mantero %A A. Zappa %T Macdonald formula for spherical functions on affine buildings %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2011 %P 669-758 %V 20 %N 4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1321/ %R 10.5802/afst.1321 %G en %F AFST_2011_6_20_4_669_0
A. M. Mantero; A. Zappa. Macdonald formula for spherical functions on affine buildings. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 4, pp. 669-758. doi : 10.5802/afst.1321. https://afst.centre-mersenne.org/articles/10.5802/afst.1321/
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