Formal degrees and adjoint 𝛾-factors

Hiraga, Kaoru; Ichino, Atsushi; Ikeda, Tamotsu

doi:10.1090/S0894-0347-07-00567-X

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: 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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