Abstract
We introduce a new construction for CAP representations for classical groups. Let τ be a cuspidal representation on GL2m(A) such that the exterior square L-function has a pole at s=1. Given a cuspidal representation σ on SP2n(A), we associate with the pair τ and σ a representation on SP2n+4m(A) which is associated with the parabolic subgroup whose Levi part is GL2m×SP2n. We show that under certain conditions the representation obtained is a CAP representation on SP2n+4m(A). The method we use is by introducing a kernel function on a big group, then using some unipotent integration we restrict to a certain dual pair which produces the lifting.
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