Explicit description of irreducible GL2(Qp)-representations over

Let p be an odd prime number. The classification of irreducible representations of GL2(Qp) over is known thanks to the works of Barthel and Livné (1995) [BL95], and Breuil (2003) [Bre03a]. 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.