Depth preserving property of the local Langlands correspondence for non-quasi-split unitary groups

In this paper, we extend our result on a depth preserving property of the local Langlands correspondence for quasi-split unitary groups ([16]) to non-quasi-split unitary groups by using the local theta correspondence. The key ingredients are a depth preserving property of the local theta correspondence proved by Pan and a description of the local theta correspondence via the local Langlands correspondence established by Gan–Ichino. To combine them, we compare splittings for metaplectic covers of unitary groups constructed by Kudla with those constructed by Pan.

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This work was carried out with the support from the Program for Leading Graduate Schools, MEXT, Japan. This work was also supported by JSPS Research Fellowship for Young Scientists and KAKENHI Grant Number 17J05451.

Received 15 April 2019

Accepted 15 January 2020

Published 24 May 2022