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Lifting of characters for nonlinear simply laced groups


Authors: Jeffrey Adams and Rebecca Herb
Journal: Represent. Theory 14 (2010), 70-147
MSC (2010): Primary 22E50; Secondary 05E99
DOI: https://doi.org/10.1090/S1088-4165-10-00361-4
Published electronically: February 1, 2010
MathSciNet review: 2586961
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Abstract: One aspect of the Langlands program for linear groups is the lifting of characters, which relates virtual representations on a group $ G$ with those on an endoscopic group for $ G$. The goal of this paper is to extend this theory to nonlinear two-fold covers of real groups in the simply laced case. Suppose $ \widetilde G$ is a two-fold cover of a real reductive group $ G$. A representation of $ \widetilde G$ is called genuine if it does not factor to $ G$. The main result is that there is an operation, denoted Lift$ _G^{\widetilde G}$, taking a stable virtual character of $ G$ to a virtual genuine character of $ \widetilde G$, and Lift$ _G^{\widetilde G}(\Theta_\pi)$ may be explicitly computed if $ \pi$ is a stable sum of standard modules.


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Additional Information

Jeffrey Adams
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: jda@math.umd.edu

Rebecca Herb
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: rah@math.umd.edu

DOI: https://doi.org/10.1090/S1088-4165-10-00361-4
Received by editor(s): June 19, 2009
Published electronically: February 1, 2010
Additional Notes: The first author was supported in part by National Science Foundation Grant #DMS-0554278
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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