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On some modular representations of the Borel subgroup of GL2(Qp)

Part of: Discontinuous groups and automorphic forms Graph theory Representation theory of groups Linear algebraic groups and related topics Lie groups

Published online by Cambridge University Press:  11 December 2009

Laurent Berger
Laurent Berger*
Affiliation:
Université de Lyon, UMPA ENS Lyon, 46 allée d’Italie, 69007 Lyon, France (email: laurent.berger@umpa.ens-lyon.fr)
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Abstract

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Colmez has given a recipe to associate a smooth modular representation Ω(W) of the Borel subgroup of GL2(Qp) to a -representation W of by using Fontaine’s theory of (φ,Γ)-modules. We compute Ω(W) explicitly and we prove that if W is irreducible and dim (W)=2, then Ω(W) is the restriction to the Borel subgroup of GL2(Qp) of the supersingular representation associated to W by Breuil’s correspondence.

Keywords

p-adic Langlands correspondencesupersingular representations(φ,Γ)-modulesGalois representations

MSC classification

Secondary: 11F80: Galois representations 05C05: Trees 11F33: Congruences for modular and $p$-adic modular forms 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11F85: $p$-adic theory, local fields 20C20: Modular representations and characters 20G25: Linear algebraic groups over local fields and their integers 22E35: Analysis on $p$-adic Lie groups 22E50: Representations of Lie and linear algebraic groups over local fields
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 1 , January 2010 , pp. 58 - 80
Copyright
Copyright © Foundation Compositio Mathematica 2009

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