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Formal degrees and adjoint $ \gamma$-factors


Authors: Kaoru Hiraga, Atsushi Ichino and Tamotsu Ikeda
Journal: J. Amer. Math. Soc. 21 (2008), 283-304
MSC (2000): Primary 22E50
DOI: https://doi.org/10.1090/S0894-0347-07-00567-X
Published electronically: June 5, 2007
Erratum: J. Amer. Math. Soc. 21 (2008), 1211-1213.
MathSciNet review: 2350057
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a conjectural formula for the formal degree of a discrete series representation in terms of the adjoint $ \gamma$-factor. Our conjecture is supported by various examples and is compatible with the Weyl dimension formula. Using twisted endoscopy, we also verify the conjecture for a stable discrete series representation of $ \operatorname{U}(3)$ over a non-archimedean local field of characteristic zero.

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Additional Information

Kaoru Hiraga
Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan
Email: hiraga@math.kyoto-u.ac.jp

Atsushi Ichino
Affiliation: Department of Mathematics, Graduate School of Science, Osaka City University, Osaka 558-8585, Japan
Email: ichino@sci.osaka-cu.ac.jp

Tamotsu Ikeda
Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan
Email: ikeda@math.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S0894-0347-07-00567-X
Received by editor(s): July 5, 2006
Published electronically: June 5, 2007
Dedicated: Dedicated to Professor Hiroshi Saito on the occasion of his sixtieth birthday
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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