In this paper we provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of “almost symplectic” representations, that is representations τ with the property that the exterior square L-function twisted by some Hecke character ω has a pole. Our theory supplements the recent work of Asgari-Shahidi on the functorial lift from GSpin2n+1 groups to GL2n.
Hundley, Joseph and Sayag, Eitan. "Descent Construction for GSpin Groups – Odd Cuspidal Case." (Jan 2009).