We determine the occurrence and explicitly describe the theta lifts on all levels of all the irreducible generic representations for the dual pair of groups $$(\text {Sp}_{2n}, \text {O}(V))$$ defined over a local nonarchimedean field $${\mathbb {F}}$$ of characteristic 0. As a direct application of our results, we are able to produce a series of non-generic unitarizable representations of these groups.

中文翻译：

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对偶对的通用表示的 Theta 提升 $$(\text {Sp}_{2n}, \text {O}(V))$$

我们确定了出现并明确描述了对双组对 $$(\text {Sp}_{2n}, \text {O}(V))$$ 定义的所有不可约泛型表示的所有级别上的 theta 提升在特征为 0 的局部非阿基米德域 $${\mathbb {F}}$$ 上。作为我们结果的直接应用，我们能够生成这些群的一系列非通用可统一表示。