Transfer of Siegel cusp forms of degree 2

Let \pi be the automorphic representation of \textrm{GSp}_4(\mathbb{A}) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and \tau be an arbitrary cuspidal, automorphic representation of \textrm{GL}_2(\mathbb{A}). Using Furusawa's integral representation for \textrm{GSp}_4\times\textrm{GL}_2 combined with a pullback formula involving the unitary group \textrm{GU}(3,3), the authors prove that the L-functions L(s,\pi\times\tau) are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations \pi have a functorial lifting to a cuspidal representation of \textrm{GL}_4(\mathbb{A}). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of \pi to a cuspidal representation of \textrm{GL}_5(\mathbb{A}). As an application, the authors obtain analytic properties of various L-functions related to full level Siegel cusp forms. They also obtain special value results for \textrm{GSp}_4\times\textrm{GL}_1 and \textrm{GSp}_4\times\textrm{GL}_2.