On certain Rankin-Selberg integrals on $GE_{6}$

Abstract

In this paper we begin the study of two Rankin-Selberg integrals defined on the exceptional group of type $GE_{6}$. We show that each factorizes and that the contribution from the unramified places is, in one case, the degree 54 Euler product $L^{S}(\pi \times \tau, E_{6} \times GL_{2}, s)$ and in the other case the degree 30 Euler product $L^{S}(\pi \times \tau, \wedge^{2} \times GL_{2}, s)$.