Descent construction for GSpin groups:  Main results and applications

Joseph Hundley; Eitan Sayag

doi:10.3934/era.2009.16.30

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

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Descent construction for GSpin groups: Main results and applications

Joseph Hundley^1, and
Eitan Sayag^2,

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

Received: November 30, 2008

Published: December 2008

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Abstract

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).

Keywords:

Langlands functoriality,
descent construction.

Mathematics Subject Classification: Primary: 32N10; Secondary: 11F70.

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