  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.
