In this paper, we investigate a relation between the Givental group of rank one and the Heisenberg–Virasoro symmetry group of the KP hierarchy. We prove, that only a two-parameter family of the Givental operators can be identified with elements of the Heisenberg–Virasoro symmetry group. This family describes triple Hodge integrals satisfying the Calabi–Yau condition. Using the identification of the elements of two groups we prove that the generating function of triple Hodge integrals satisfying the Calabi–Yau condition and its $\Theta$-version are tau-functions of the KP hierarchy. This generalizes the result of Kazarian on KP integrability in the case of linear Hodge integrals.

中文翻译：

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三重霍奇积分的 KP 可积性，I. 从 Givental 群到层次对称

在本文中，我们研究了排名第一的 Givental 群与 KP 层次结构的 Heisenberg-Virasoro 对称群之间的关系。我们证明，只有 Givental 算子的两个参数族可以与 Heisenberg-Virasoro 对称群的元素识别。该族描述满足 Calabi-Yau 条件的三重 Hodge 积分。利用两组元素的识别，我们证明了满足 Calabi-Yau 条件的三重 Hodge 积分的生成函数及其 $\Theta$-version 是 KP 层次结构的 tau 函数。这概括了 Kazarian 在线性霍奇积分情况下对 KP 可积性的结果。