Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local distinction, quadratic base change and automorphic induction for
  $\mathrm{GL_n}$   Behind this sophisticated title hides an elementary exercise on Clifford
theory for index two subgroups and self-dual/conjugate-dual representations.
When applied to semi-simple representations of the Weil-Deligne group $W'_F$ of
a non Archimedean local field $F$, and further translated in terms of
representations of $\mathrm{GL_n}(F)$ via the local Langlands correspondence
when $F$ has characteristic zero, it yields various statements concerning the
behaviour of different types of distinction under quadratic base change and
automorphic induction. When $F$ has residual characteristic different from $2$,
combining of one of the simple results that we obtain with the tiviality of
conjugate-orthogonal root numbers (proved by Gan, Gross and Prasad), we recover
without using the LLC a result of Serre on the parity of the Artin conductor of
orthogonal representations of $W'_F$. On the other hand we discuss its parity
for symplectic representations using the LLC and the Prasad and Takloo-Bighash
conjecture.

27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con