## Lifting of characters for nonlinear simply laced groups

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- by Jeffrey Adams and Rebecca Herb
- Represent. Theory
**14**(2010), 70-147 - DOI: https://doi.org/10.1090/S1088-4165-10-00361-4
- Published electronically: February 1, 2010
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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 $\text {Lift}_G^{\widetilde G}$, taking a stable virtual character of $G$ to a virtual genuine character of $\widetilde G$, and $\text {Lift}_G^{\widetilde G}(\Theta _\pi )$ may be explicitly computed if $\pi$ is a stable sum of standard modules.## References

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## Bibliographic 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
- MR Author ID: 84600
- Email: rah@math.umd.edu
- 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
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**14**(2010), 70-147 - MSC (2010): Primary 22E50; Secondary 05E99
- DOI: https://doi.org/10.1090/S1088-4165-10-00361-4
- MathSciNet review: 2586961