227 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
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
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
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