A Rankin-Selberg integral for the adjoint representation of \(GL_ 3\) (Q1177417)

This paper deals with some problems towards the analytic continuation and functional equation of the \(L\)-function \(L(s,\pi,r)\) attached to a cuspidal representation of \(GL_ 3\) and the eight dimensional adjoint representation \(r\) of the \(L\)-group \(GL_ 3(\mathbb{C})\) of \(GL_ 3\). The Basic Identity is established for the global zeta-integral; the latter one is shown to be Eulerian with Whittaker model. Then the unramified local zeta-integrals are compared with the Langlands factors. In all this basic use is made of the embedding of \(SL_ 3\) into \(G_ 2\).