Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal hierarchical structure of reducibility of Harish-Chandra
  parabolic induction   Given a supercuspidal representation $\sigma$ of a parabolic subgroup $P$ of
reductive group $G$, we discover a universal hierarchical structure of
reducibility of the parabolic induction $Ind^G_P(\sigma)$, i.e. always
irreducible from some Levi-level up. As its applications, we provide a new
simple proof of the generic irreducibility property of parabolic induction, and
prove Clozel's finiteness conjecture of special exponents under some
conditions. Indeed, those conditions are predicted by two conjectures of
Shahidi which in some sense are proved for classical groups by Arthur in his
monumental book--The Endoscopic Classification of Representations: Orthogonal
and Symplectic Groups. At last, naturally, such type simple beautiful structure
theorem should be conjectured to hold in general, i.e. if the "reducibility
conditions" of a general parabolic induction lies in some Levi subgroup, then
it is always irreducible from this Levi up.

24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th