Modulo p parabolic induction of pro-p-Iwahori Hecke algebra

Abstract

Abstract We study the structure of parabolic inductions of a pro-p-Iwahori Hecke algebra. In particular, we give a classification of irreducible modulo p representations of pro-p-Iwahori Hecke algebras in terms of supersingular representations. Since supersingular representations are classified by Ollivier and Vignéras, it completes the classification of irreducible modulo p representations.