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 0 . As an application, we prove the formal degree conjecture of Hiraga, Ichino and Ikeda for the non-split inner forms of S p 4 \mathrm {Sp}_4 and G S p 4 \mathrm {GSp}_4 .
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