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arXiv · 2012.04219

Formal degrees and the local theta correspondence: the quaternionic case

Hirotaka Kakuhama
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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 quaternionic 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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Hirotaka Kakuhama. 2020-12-08. Formal degrees and the local theta correspondence: the quaternionic case. https://arxiv.org/abs/2012.04219

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