Des représentations modulo p de GL(2,D), D algèbre à division sur un corps local

Let p be a prime number. Let F be a non-Archimedean locally compact local field of residue characteristic p and D be a finite dimensional division algebra with center F. We give an irreducibility criterion for parabolically induced representations of GL(2,D) over F¯p and classify (up to the supersingular ones) the irreducible smooth admissible representations of GL(2,D) over F¯p. This generalizes previous works of Barthel-Livné for the split GL(2,F).