Representations of a p-adic group in characteristic p

2017/12/21 by Henniart, G., Vignéras, M. -F.
#11 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1712.08038

Abstract

Let F be a locally compact non-archimedean field of residue characteristic p, G a connected reductive group over F, and R a field of characteristic p. When R is algebraically closed, the irreducible admissible R-representations of G=G(F) are classified in term of supersingular R-representations of the Levi subgroups of G and parabolic induction; there is a similar classification for the simple modules of the pro-p Iwahori Hecke R-algebra. In this paper, we show that both classifications hold true when R is not algebraically closed.

Related

• Modulo p representations of reductive p-adic groups: functorial properties
• Modulo ℓ-representations of p-adic groups SL_n(F)
• On pro-p-Iwahori invariants of R-representations of reductive p-adic groups
• Types for tame p-adic groups
• Non-admissible irreducible representations of p-adic GL_n in characteristic p