# American Institute of Mathematical Sciences

2009, 16: 30-36. doi: 10.3934/era.2009.16.30

## Descent construction for GSpin groups: Main results and applications

 1 Mathematics Department, Mailcode 4408, Southern Illinois University Carbondale, 1245 Lincoln Drive, Carbondale, IL 62901, United States 2 Department of Mathematics, Ben Gurion University of Negev, PO Box 653, Be’er Sheva 84105, Israel

Received  December 2008 Published  May 2009

The purpose of this note is to announce an extension of the descent method of Ginzburg, Rallis, and Soudry to the setting of essentially self dual representations. This extension of the descent construction provides a complement to recent work of Asgari and Shahidi [2] on the generic transfer for general Spin groups as well as to the work of Asgari and Raghuram [1] on cuspidality of the exterior square lift for representations of $GL_4$. Complete proofs of the results announced in the present note will appear in our forthcoming article(s).
Citation: Joseph Hundley, Eitan Sayag. Descent construction for GSpin groups: Main results and applications. Electronic Research Announcements, 2009, 16: 30-36. doi: 10.3934/era.2009.16.30
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