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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Lifting of characters for nonlinear simply laced groups
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by Jeffrey Adams and Rebecca Herb PDF
Represent. Theory 14 (2010), 70-147 Request permission

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.
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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
  • 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