In this paper we provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of “almost orthogonal” representations, that is representations τ with the property that the symmetric 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 (split and quasisplit forms of) GSpin2n to GL2n.
Hundley, Joseph and Sayag, Eitan. "Descent Construction for GSpin Groups – Even Case." (Jan 2009).