  Let E/F be a quadratic extension of non-archimedean local fields of
characteristic 0. In this paper, we investigate two approaches which attempt to
describe the smooth irreducible representations of GL(n,E) that are
distinguished by its subgroup GL(n,F). One relates this class to
representations which come as base change lifts from a quasi-split unitary
group F, while another deals with a certain symmetry condition. By
characterizing the union of images of the base change maps we show that these
two approaches are closely related. Using this observation, we are able to
prove a statement relating base change and distinction for ladder
representations. We then produce a wide family of examples in which the
symmetry condition does not impose GL(n,F)-distinction, and thus exhibit the
limitations of these two approaches.
