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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Lifting of characters for nonlinear simply laced groups
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by Jeffrey Adams and Rebecca Herb
Represent. Theory 14 (2010), 70-147
Published electronically: February 1, 2010


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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Bibliographic Information
  • Jeffrey Adams
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
  • Email:
  • Rebecca Herb
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
  • MR Author ID: 84600
  • Email:
  • 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:
  • MathSciNet review: 2586961