Descent construction for GSpin groups: Main results and applications

The purpose of this note is to announce an extension of thedescent method of Ginzburg, Rallis, and Soudry to the setting of essentially self dual representations. This extension of thedescent construction provides a complement to recent work ofAsgari and Shahidi [2]on the generic transfer for general Spin groups as well as to thework of Asgari and Raghuram [1] on cuspidalityof the exterior square lift for representations of $GL_4$.Complete proofs of the results announced in the present note willappear in our forthcoming article(s).