Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modulo $p$ representations of reductive $p$-adic groups: functorial
  properties   Let $F$ be a local field with residue characteristic $p$, let $C$ be an
algebraically closed field of characteristic $p$, and let $\mathbf{G}$ be a
connected reductive $F$-group. In a previous paper, Florian Herzig and the
authors classified irreducible admissible $C$-representations of
$G=\mathbf{G}(F)$ 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 $\tau$ of $M$, we determine the
lattice of subrepresentations of $\mathrm{Ind}_P^G \tau$ and we show that
$\mathrm{Ind}_P^G \chi \tau$ is irreducible for a general unramified character
$\chi$ of $M$. In the reverse direction, we compute the image by the two
adjoints of $\mathrm{Ind}_P^G$ of an irreducible admissible representation
$\pi$ of $G$. On the way, we prove that the right adjoint of $\mathrm{Ind}_P^G
$ respects admissibility, hence coincides with Emerton's ordinary part functor
$\mathrm{Ord}_{\overline{P}}^G$ on admissible representations.

3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ