Formal degrees and the local theta correspondence: the quaternionic case

2020/12/08 by Kakuhama, Hirotaka
#11F27 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2012.04219

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 Sp₄ and \rm GSp₄.

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