Cocenters and representations of pro-𝑝 Hecke algebras

Abstract

Abstract. In this paper, we study the relation between the cocenterH and the representations of an affine pro-p Hecke algebraH =H(0, −). As a consequence, we obtain a new criterion on supersingular representations: a (virtual) representation ofH is supersingular if and only if its character vanishes on the non-supersingular part of the cocenterH.