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