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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Formal degrees and adjoint $\gamma$-factors
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by Kaoru Hiraga, Atsushi Ichino and Tamotsu Ikeda PDF
J. Amer. Math. Soc. 21 (2008), 283-304 Request permission

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
  • MR Author ID: 680344
  • 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
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 21 (2008), 283-304
  • MSC (2000): Primary 22E50
  • DOI: https://doi.org/10.1090/S0894-0347-07-00567-X
  • MathSciNet review: 2350057