We study a relation between distinction and special values of
local invariants for representations of the general linear group
over a quadratic extension of $p$-adic fields.
We show that the local Rankin-Selberg root number of any pair
of distinguished representation is trivial and as a corollary
we obtain an analogue for the global root number of any pair
of distinguished cuspidal representations. We further study the
extent to which the gamma factor at $1/2$ is trivial for distinguished
representations as well as the converse problem.
distinguished representation, local constant
11F70 - Representation-theoretic methods; automorphic representations over local and global fields