Selected Topics in Algebra (V5A2) -Smooth representations of p-adic reductive groups - Wintersemester 2015/16

Dr. Eugen Hellmann
E-mail: hellmann (add

Monday 10-12h, MZ 0.006
First lecture: 19.10.2015


In this lecture course we want to study representations of p-adic reductive group, i.e. groups like GLn(Qp). We will introduce the important class of so called smooth representations, i.e. representation on a vector space V such that every element of V has open stabilizer. These representations show up in the Langlands program and the theory of automorphic forms.

We plan to cover the following topics:

  • Smooth and admissible representations
  • Hecke algebras and the Satake transform
  • Unramified representations and their relation with modules over the Hecke algebra
  • Parabolic induction


Representation theory of finite groups, some knowledge about linear algebraic groups and reductive groups, basis knowledge about local fields.


  • C. Bushnell, G. Henniart: The local Langlands Conjecture for GL(2), Grundlehren der Math. Wissenschaften 335, Springer
  • P. Cartier: Representations of p-adic groups: a survey, in Automorphic forms, representations and L-functions, Proc. Symp. Pure Math. 33, AMS
  • S. Kudla: The local Langlands correspondence: the non-archimedean case, in Motives , Proc. Symp. Pure Math. 55, AMS
  • D. Renard: Represéntations des groupes réductifs p-adique, Cours spécialisés 17, Publications de la SMF
  • M.-F. Vignéras: Represéntations l-modulaires d'un groupe réductif p-adique avec l≠p , Progr. in Math. 137, Birkhäuser

Last modified: 19. 10. 2015, Eugen Hellmann