Distinguished representations, base change, and reducibility for unitary groups

By U. K. Anandavardhanan, C. Rajan. 2004

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We show the equality of the local Asai L-functions defined via the Rankin-Selberg method and the Langlands-Shahidi method for a square-integrable representation of GL n (E). As a consequence, we characterize reducibility of certain induced representations of U(n,n), and the image of the base change map from U(n) to GL n (E) in terms of GL n (F)-distinguishedness. We also determine precisely when the Steinberg representation of GL n (E) is distinguished with respect to a character of F ∗ .

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0876006fe3298503749de4091d0289cb455dc686