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

Abstract

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.

32 pages, published version

References in corpus (2)

• Instantons and Merons in Matrix Models
• Cubic Hodge integrals and integrable hierarchies of Volterra type

Cited by in corpus (1)

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