论文标题
三重杂货积分的KP集成性。 I.从吉维尔组到层次结构对称性
KP integrability of triple Hodge integrals. I. From Givental group to hierarchy symmetries
论文作者
论文摘要
在本文中，我们调查了KP层次结构的吉维尔·吉维尔斯一组与海森伯格 - 维拉索罗对称群体之间的关系。我们证明，只有一个赠送运营商的两个参数家族才能通过海森伯格 - 维拉索罗对称群体的元素来识别。这个家庭描述了满足卡拉比野条件的三重杂货积分。使用两个组的元素的识别，我们证明了满足Calabi-yau条件的三重杂货积分的生成函数及其$θ$ version是KP层次结构的tau功能。这概括了Kazarian在线性Hodge积分的情况下对KP的可集成性的结果。
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 $Θ$-version are tau-functions of the KP hierarchy. This generalizes the result of Kazarian on KP integrability in the case of linear Hodge integrals.
