• Corpus ID: 118396896

Automorphic representations and harmonic cochains for $GL_{n+1}$

  title={Automorphic representations and harmonic cochains for \$GL\_\{n+1\}\$},
  author={Yacine Ait Amrane},
  journal={arXiv: Representation Theory},
Let $K$ be a global field of positive characteristic. Let $\infty$ be a fixed place of $K$. This paper gives an explicit isomorphism between the space of automorphic forms (resp. cusp forms) for $GL_{n+1}(K)$ that transform like the special representations and certain spaces of harmonic cochains (resp. those with finite support) defined on the Bruhat-Tits building of $GL_{n+1}(K_\infty)$. 


Residues on buildings and de Rham cohomology of p-adic symmetric domains
The cohomology of Drinfeld’s p-adic symmetric domain was computed by P. Schneider and U. Stuhler in 1991. Here we propose a more explicit and combinatorial approach based on a notion of residue of a
Cohomology of Drinfeld symmetric spaces and Harmonic cochains
Soit K un corps local non-archimedien. Ce papier donne un isomorphisme explicite entre le dual de la representation speciale de GL n+1 (K) et l'espace des cocycles harmoniques definis sur l'immeuble
Buildings and Classical Groups
monograph on Bruhat-TIts buildings attached to classical groups. Both spherical and affine buildings.
Chevalley Groups Over Function Fields and Automorphic Forms
Stuhler : The cohomology of p-adic symmetric spaces, Inv
  • El Alia BP ,
  • 1991
Reversat : Automorphic forms and Drinfeld’s reciprocity law, Lecture 11, in ”Drinfeld modules, modular schemes and applications
  • Proceedings of the Workshop at Alden-Biesen
  • 1996
Drinfel’d : Elliptic Modules, Math
  • USSR Sbornik 23,
  • 1974
Automorphic forms and Drinfeld ’ s reciprocity law , Lecture 11 , in ” Drinfeld modules , modular schemes and applications ”
  • Proceedings of the Workshop at Alden - Biesen 9 - 14 sept .
  • 2000