Explicit description of irreducible GL2(Qp)-representations over Fp

Stefano Morra (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Let p be an odd prime number. The classification of irreducible representations of GL2 (Qp ) over Fp is known thanks to the works of Barthel-Livné and Breuil. In the present paper we illustrate an exhaustive description of such irreducible representations, through the study of certain functions on the Bruhat-Tits tree of GL2 (Qp ). In particular, we are able to detect the socle filtration for the KZ-restriction of supersingular representations, principal series and special series.

Mots clés: P-adic Langlands correspondence; Supersingular representation.; Supersingular representation

Domaines: Théorie des nombres [math.NT]; Théorie des représentations [math.RT]

Stefano Morra. Explicit description of irreducible GL2(Qp)-representations over Fp. Journal of Algebra, 2011, 339 (1), pp.252-303. ⟨10.1016/j.jalgebra.2011.02.043⟩. ⟨hal-00576943v2⟩