Rankin-Selberg integral with Non-unique model for the standard   L-function of $G_2$
  Let L^S(\pi,s,st) be a partial L-function of degree 7 of a cuspidal automorphic representation \pi of the exceptional group G_2. Here we construct a Rankin-Selberg integral for representations having certain Fourier coefficient. 
Nadya Gurevich and Avner Segal
math.RT