Let F be a local field with residue characteristic p, let C be an
algebraically closed field of characteristic p, and let G be a
connected reductive F-group. In a previous paper, Florian Herzig and the
authors classified irreducible admissible C-representations of
G=G(F) in terms of supercuspidal representations of Levi subgroups
of G. Here, for a parabolic subgroup P of G with Levi subgroup M and an
irreducible admissible C-representation τ of M, we determine the
lattice of subrepresentations of IndPGτ and we show that
IndPGχτ is irreducible for a general unramified character
χ of M. In the reverse direction, we compute the image by the two
adjoints of IndPG of an irreducible admissible representation
π of G. On the way, we prove that the right adjoint of IndPG respects admissibility, hence coincides with Emerton's ordinary part functor
OrdPG on admissible representations.Comment: 39 page