Stability of local gamma factors arising from the doubling method for general spin groups.

The doubling method of Piatetski-Shapiro and Rallis enables one to define local factors for irreducible non-generic representations of classical groups, using an integral representation. In this work, we prove the stability property of the gamma factor for split general spin groups. This result can be used for the proof of a weak functorial lift, from cuspidal representations of general spin groups to automorphic representations of the appropriate general linear group, by virtue of the generalized doubling method. We obtain our result by adapting the method of Rallis and Soudry, who obtained the stability for orthogonal and symplectic groups.