Let E/F be a quadratic separable extension of non-archimedean
local fields. The group Sp(2n,F) sits inside both GL(2n,F) and U(2n,F)
(the quasi-split unitary group with respect to the extension E/F) as a
closed subgroup. This talk is about Sp(2n,F)-distinguished representations
of the aforementioned groups. I will begin by motivating the question of
classifying distinguished representations for general symmetric spaces
after which we will look into some specific classification results for
Sp(2n,F)-distinguished representations of these two groups.