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In [F-J], Friedberg and Jacquet introduce a relative trace formula which gives the lifting from the cuspidal representations of GSp2 to the selfcontragradient cuspidal representations of GL4. In this paper, we prove the fundamental lemma for this trace formula, meanwhile illustrate the method of using Weil representation in computing local integrals. What we emphasize here is the method of the proof. It can be applied to show fundamental lemma for many other relative trace formulas, which are out of the scope of previously available methods. (1.1) Let F be a number field, A its adele ring. Let τn be a n×n matrix with 1’s on the antidiagonal and 0’s elsewhere. The group GSp2(F ) is the similitude group associated to the symplectic form w0 = [ τ2 −τ2 ] . The

The induced Weil representation and the Shalika period