COCENTERS AND REPRESENTATIONS OF PRO-p HECKE ALGEBRAS.

In this paper, we study the relation between the cocenter ^∼H and the representations of an affine pro-p Hecke algebra ^∼H = ^∼H (0,-). As a consequence, we obtain a new criterion on supersingular representations: a (virtual) representation of ^∼H is supersingular if and only if its character vanishes on the non-supersingular part of the cocenter ^∼H. [ABSTRACT FROM AUTHOR]