Distinguished Generic Representations of GL(n) over p-adic Fields

Let K/F be a quadratic extension of p-adic fields, and n a positive integer. A smooth irreducible representation of the group GL(n, K) is said to be distinguished, if it admits on its space a nonzero GL(n, F)-invariant linear form. In the present work, we classify distinguished generic representations of the group GL(n, K) in terms of inducing quasi-square-integrable representations. This has, as a consequence, the truth of the expected equality between the Rankin-Selberg type Asai L-function of a generic representation and the Asai L-function of its Langlands parameter.