Corpus ID: 227747423

Formal degrees and local theta correspondence: quaternion case

@article{Kakuhama2020FormalDA,
  title={Formal degrees and local theta correspondence: quaternion case},
  author={Hirotala Kakuhama},
  journal={arXiv: Number Theory},
  year={2020}
}
In this paper, we determine a constant occurring in a local analogue of the Siegel-Weil formula, and describe the behavior of the formal degree under the local theta correspondence for quaternion dual pairs 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-Ikeda for the non-split inner forms of ${\rm Sp}_4$ and ${\rm GSp}_4$. 

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