Complementary results on the Rankin-Selberg gamma factors of classical groups

Let G be an orthogonal or symplectic group, defined over a local field, or the metaplectic group. We study the gamma-factor for a pair of irreducible generic representations of G x GL(n), defined using the Rankin-Selberg method. In the metaplectic case we use Shimura type integrals. We prove that the gamma-factor satisfies a list of fundamental properties, stated by Shahidi, which define it uniquely. In particular, we show full multiplicativity for symplectic and metaplectic groups. It is important for applications to relate this gamma-factor to the one arising from the Langlands-Shahidi method. As a corollary of our results, these factors coincide. This is a refinement of previous works on orthogonal groups, showing such an equality up to certain normalization factors. (C) 2014 Elsevier Inc. All rights reserved.