In this paper, we study the first-order cohomology space of countable direct limit groups related to Olshanski spherical pairs, relatively to unitary representations which do not have almost invariant vectors. In particular, we prove a variant of Delorme’s vanishing result of the first-order cohomology space for spherical representations of Olshanski spherical pairs.

中文翻译：

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Olshanski球对上一阶上同调的消失

在本文中，我们研究了与 Olshanski 球面对相关的可数直接极限群的一阶上同调空间，相对于不具有几乎不变向量的酉表示。特别是，我们证明了 Delorme 的一阶上同调空间消失结果的变体，用于 Olshanski 球面对的球面表示。