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.

中文翻译：

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非准分裂unit群的本地Langlands对应关系的深度保留性质

在本文中，我们通过使用局部theta对应关系，将拟裂Lang单元（[16]）到非拟裂unit单元的本地Langlands对应关系的深度保持性质扩展了我们的结果。关键要素是Pan证明的局部theta对应关系的深度保留性质，以及由Gan–Ichino建立的局部Langlands对应关系描述局部theta对应关系。为了将它们组合起来，我们比较了库德拉（Kudla）和潘（Pan）所建立的groups群的元组盖的分裂。