We give upper bounds on limit multiplicities of certain nontempered representations of unitary groups $U(a,b)$, conditionally on the endoscopic classification of representations. Our result applies to some cohomological representations, and we give applications to the growth of cohomology of cocompact arithmetic subgroups of unitary groups. The representations considered are transfers of products of characters and discrete series on endoscopic groups, and the bounds are obtained using Arthur’s stabilization of the trace formula and the classification established by Mok, and Kaletha, Minguez, Shin and White.

中文翻译：

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酉群的极限重数和稳定迹公式

我们给出酉群的某些非调和表示的极限重数的上限$U（A,乙）$，有条件地基于表征的内窥镜分类。我们的结果适用于一些上同调表示，并且我们将其应用于酉群的协紧算术子群的上同调增长。所考虑的表示是内窥镜组上特征和离散系列的乘积的传递，并且使用 Arthur 的迹稳定公式和 Mok、Kaletha、Minguez、Shin 和 White 建立的分类来获得界限。