Abstract
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.