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Tempered endoscopy for real groups III: Inversion of transfer and $L$-packet structure

Author: D. Shelstad
Journal: Represent. Theory 12 (2008), 369-402
MSC (2000): Primary 22E45, 22E50
Published electronically: October 17, 2008
MathSciNet review: 2448289
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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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D. Shelstad
Affiliation: Department of Mathematics, Rutgers University, Newark, New Jersey 07102

Received by editor(s): January 15, 2008
Published electronically: October 17, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.