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

TL;DR

This paper proves the stability of local gamma factors from the doubling method for split general spin groups, which is crucial for constructing global functorial lifts in automorphic forms.

Contribution

It extends the stability property of gamma factors to general spin groups, adapting methods from symplectic and orthogonal cases.

Findings

Proves stability of local gamma factors for split general spin groups.

Adapts existing proofs from symplectic and orthogonal groups.

Supports the application of the doubling method in automorphic lifting.

Abstract

In this work we prove that the local $\gamma$-factor arising from the doubling integrals for split general spin groups is stable. This deep property of the $\gamma$-factor constitutes an important ingredient in the application of the (generalized) doubling method to the construction of a global functorial lift. We obtain our result by adapting the arguments of Rallis and Soudry who proved the stability property for symplectic and orthogonal groups.