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
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by Kaoru Hiraga, Atsushi Ichino and Tamotsu Ikeda

J. Amer. Math. Soc. 21 (2008), 283-304

DOI: https://doi.org/10.1090/S0894-0347-07-00567-X

Published electronically: June 5, 2007

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Erratum: J. Amer. Math. Soc. 21 (2008), 1211-1213.

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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