Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-dual representations with vectors fixed under an Iwahori subgroup   Let $G$ be the group of $F$-points of a split connected reductive $F$-group
over a non-Archimedean local field $F$ of characteristic 0. Let $\pi$ be an
irreducible smooth self-dual representation of $G$. The space $W$ of $\pi$
carries a non-degenerate $G$-invariant bilinear form $(\,,\,)$ which is unique
up to scaling. The form is easily seen to be symmetric or skew-symmetric and we
set $\varepsilon({\pi})=\pm 1$ accordingly. In this article, we show that
$\varepsilon{(\pi)}=1$ when $\pi$ is a generic representation of $G$ with
non-zero vectors fixed under an Iwahori subgroup $I$.

22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th