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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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Tempered endoscopy for real groups III: Inversion of transfer and $L$-packet structure
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by D. Shelstad PDF
Represent. Theory 12 (2008), 369-402 Request permission

Abstract:

This paper examines adjoint relations for spectral analogues of the geometric transfer factors of Langlands and Shelstad in the case of the tempered spectrum of a real reductive algebraic group where the complex points are connected. Each tempered irreducible character is then expanded explicitly in terms of endoscopic characters. The analysis is also reinterpreted in terms of structure on $L$-packets in the form conjectured recently in much greater generality by Arthur. A triviality result is proved for the Whittaker normalization of spectral transfer factors which simplifies the results for certain inner forms of a quasi-split group.
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Additional Information
  • D. Shelstad
  • Affiliation: Department of Mathematics, Rutgers University, Newark, New Jersey 07102
  • Email: shelstad@rutgers.edu
  • Received by editor(s): January 15, 2008
  • Published electronically: October 17, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 12 (2008), 369-402
  • MSC (2000): Primary 22E45, 22E50
  • DOI: https://doi.org/10.1090/S1088-4165-08-00337-3
  • MathSciNet review: 2448289