44 research outputs found
Modular representations of p-adic groups
I will survey some results in the theory of modular representations of a
reductive -adic group, in positive characteristic and
The pro-p-Iwahori–Hecke algebra of a reductive p-adic group, II
For any commutative ring R and any reductive p-adic group G, we describe the center of the pro-p-Iwahori–Hecke R-algebra of G. We show that the pro-p-Iwahori–Hecke algebra is a finitely generated module over its center and is a finitely generated R-algebra. When the ring R is noetherian, the center is a finitely generated R-algebra and the pro-p-Iwahori–Hecke R-algebra is noetherian. This generalizes results known only for split groups
Modulo representations of reductive -adic groups: functorial properties
Let be a local field with residue characteristic , let be an
algebraically closed field of characteristic , and let be a
connected reductive -group. In a previous paper, Florian Herzig and the
authors classified irreducible admissible -representations of
in terms of supercuspidal representations of Levi subgroups
of . Here, for a parabolic subgroup of with Levi subgroup and an
irreducible admissible -representation of , we determine the
lattice of subrepresentations of and we show that
is irreducible for a general unramified character
of . In the reverse direction, we compute the image by the two
adjoints of of an irreducible admissible representation
of . On the way, we prove that the right adjoint of respects admissibility, hence coincides with Emerton's ordinary part functor
on admissible representations.Comment: 39 page
Representations of a reductive -adic group in characteristic distinct from
We investigate the irreducible cuspidal -representations of a reductive
-adic group over a field of characteristic different from . When
is algebraically closed, for many groups , a list of cuspidal -types
has been produced satisfying exhaustion, sometimes for a
restricted kind of cuspidal representations, and often unicity. We verify that
those lists verify Aut()-stability and we produce similar lists when is
no longer assumed algebraically closed. Our other main results concern
supercuspidality. This notion makes sense for the representations in
the cuspidal -types as above, which involve finite reductive
groups. We check that an irreducible cuspidal representation of induced
from is supercuspidal if and only is supercuspidal.Comment: 45 pages This is the final versio