Cohomology of Drinfeld symmetric spaces and Harmonic cochains
Annales de l'Institut Fourier, Volume 56 (2006) no. 3, pp. 561-597.

Let K be a non-archimedean local field. This paper gives an explicit isomorphism between the dual of the special representation of GL n+1 (K) and the space of harmonic cochains defined on the Bruhat-Tits building of GL n+1 (K), in the sense of E. de Shalit [11]. We deduce, applying the results of a paper of P. Schneider and U. Stuhler [9], that there exists a GL n+1 (K)-equivariant isomorphism between the cohomology group of the Drinfeld symmetric space and the space of harmonic cochains.

Soit K un corps local non-archimédien. Ce papier donne un isomorphisme explicite entre le dual de la représentation spéciale de GL n+1 (K) et l’espace des cocycles harmoniques définis sur l’immeuble de Bruhat-Tits de GL n+1 (K), au sens de E. de Shalit [11]. Nous déduisons, en appliquant les résultats d’un papier de P. Schneider et U. Stuhler [9], qu’il existe un isomorphisme GL n+1 (K)-équivariant entre le groupe de cohomologie de l’espace symétrique de Drinfeld et l’espace des cocycles harmoniques.

DOI: 10.5802/aif.2194
Classification: 22E50, 20E42
Keywords: Drinfeld symmetric spaces, cohomology, Bruhat-Tits buildings, harmonic cochains, special representations
Aït Amrane, Yacine 1

1 Universität Münster Mathematisches Institut Einsteinstr. 62 48149 Münster (Allemagne)
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Aït Amrane, Yacine. Cohomology of Drinfeld symmetric spaces and Harmonic cochains. Annales de l'Institut Fourier, Volume 56 (2006) no. 3, pp. 561-597. doi : 10.5802/aif.2194. https://aif.centre-mersenne.org/articles/10.5802/aif.2194/

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