Formal degrees and the local theta correspondence: The quaternionic case

Kakuhama, Hirotaka

doi:10.1090/ert/630

Formal degrees and the local theta correspondence: The quaternionic case
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by Hirotaka Kakuhama

Represent. Theory 26 (2022), 1192-1267

DOI: https://doi.org/10.1090/ert/630

Published electronically: December 20, 2022

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Abstract:

In this paper, we determine a constant occurring in a local analogue of the Siegel-Weil formula, and describe the behavior of the formal degrees under the local theta correspondence for a quaternionic dual pair of almost equal rank over a non-Archimedean local field of characteristic $0$. As an application, we prove the formal degree conjecture of Hiraga, Ichino and Ikeda for the non-split inner forms of $\mathrm {Sp}_4$ and $\mathrm {GSp}_4$.

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