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

@article{Alexandrov2020KPIO, title={KP integrability of triple Hodge integrals, I. From Givental group to hierarchy symmetries}, author={A. Alexandrov}, journal={arXiv: Mathematical Physics}, year={2020} }

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… Expand

#### 3 Citations

KP hierarchy for Hurwitz-type cohomological field theories

- Mathematics, Physics
- 2021

We generalise a result of Kazarian regarding Kadomtsev-Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting problems or… Expand

KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions

- Mathematics, Physics
- 2021

In this paper, we continue our investigation of the triple Hodge integrals satisfying the Calabi–Yau condition. For the tau-functions, which generate these integrals, we derive the complete families… Expand

KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model

- Physics, Mathematics
- 2020

In this paper we introduce a new family of the KP tau-functions. This family can be described by a deformation of the generalized Kontsevich matrix model. We prove that the simplest representative of… Expand

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