Macdonald formula for spherical functions on affine buildings
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 4, p. 669-758

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 = {Mantero, A. M. and Zappa, A.},
     title = {Macdonald formula for spherical functions on affine buildings},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 20},
     number = {4},
     year = {2011},
     pages = {669-758},
     doi = {10.5802/afst.1321},
     mrnumber = {2918211},
     zbl = {1247.43012},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2011_6_20_4_669_0}
}
Mantero, A. M.; Zappa, A. 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. http://www.numdam.org/item/AFST_2011_6_20_4_669_0/

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