KP integrability of triple Hodge integrals, I. From Givental group to hierarchy symmetries

A. Alexandrov
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引用次数: 10

Abstract

In this paper we investigate a relation between the Givental group of rank one and 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 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 case of linear Hodge integrals.
三重Hodge积分的KP可积性,1 .从给定群到层次对称
本文研究了KP层次的1阶给定群与Heisenberg-Virasoro对称群之间的关系。我们证明了只有两个参数的给定算子族可以用Heisenberg-Virasoro对称群的元素来标识。这个族描述了满足Calabi-Yau条件的三重Hodge积分。通过对两群元的辨识,证明了满足Calabi-Yau条件的三重Hodge积分的生成函数及其$\Theta$-版本是KP层次的tau函数。推广了Kazarian关于线性Hodge积分KP可积性的结论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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