Multiplicativity of the gamma factors of Rankin-Selberg integrals for SO_2l × GL_n

Let SO _2l be the special even orthogonal group, split or quasi-split, defined over a local non-Archimedian field. The Rankin-Selberg method for a pair of generic representations of SO _2l × GL _nconstructs a family of integrals, which are used to define γ and L-factors. Here we prove full multiplicative properties for the γ-factor, namely that it is multiplicative in each variable. As a corollary, the γ-factor is identical with Shahidi's standard γ-factor.