LAUSR

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 ( 2 n , E ) is the unstable base change lift of a generic cuspidal automorphic representation σ of the quasi-split unitary group U ( 2 n ) if and only if it is distinguished by GL ( 2 n , 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.