Quaternion distinguished representations and unstable base change for unitary groups

Abstract

Let E/F be a quadratic extension of number fields and D a quaternion algebra over F which E embeds. Flicker and Rallis conjectured that a cuspidal automorphic representation π of GL(2n,E) is the unstable base change lift of a generic cuspidal automorphic representation σ of the quasi-split unitary group U(2n) if and only if it is distinguished by GL(2n,F). We conjecture that π is distinguished by GL(n,D) if and only if σ is generic with respect to certain non-degenerate character attached to D. We use the relative trace formula to prove the n=1 case of our conjecture.