Distinction and Asai $L$-functions for generic representations of general linear groups over p-adic fields

Abstract

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 genric distinguished 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.

References in corpus (2)

• Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields
• Distinguished representations and exceptional poles of the Asai-L-function

Cited by in corpus (1)

• Plancherel formula for ${\mathrm{GL}}_n(F)\backslash {\mathrm{GL}}_n(E)$ and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups