论文标题
正式学位和当地的theta信函：Quaternionic情况
Formal degrees and the local theta correspondence: the quaternionic case
论文作者
论文摘要
在本文中，我们确定了在siegel-weil公式的局部类似物中发生的常数，并描述了局部theta对应的正式学位的行为，用于在特征性$ 0 $ 0 $ 0的非Archimedean本地领域的Quaternionic Dual对几乎相等等级的Quaternionic Dual对。作为一个应用程序，我们证明了hiraga-ichino-ikeda的正式猜想，用于$ {\ rm sp} _4 $和$ {\ rm gsp} _4 $的非切片内部形式。
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 ${\rm GSp}_4$.
