Explicit description of irreducible [formula omitted]-representations over [formula omitted

Abstract

Let p be an odd prime number. The classification of irreducible representations of GL 2 ( Q p ) over F ¯ p 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 GL 2 ( Q p ) . In particular, we are able to detect the socle filtration for the KZ-restriction of supersingular representations, principal series and special series.