Cap representations of G 2 and the spin L-function of PGS p6

Abstract

We give a construction of a family of CAP representations of the exceptional group G2, whose existence is predicted by Arthur’s conjecture. These are constructed by lifting certain cuspidal representations of PGSp6. To show that the lifting is non-zero, we establish a Rankin-Selberg integral for the degree 8 Spin L-function of these cuspidal representations of PGSp6.