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

Abstract

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 this family describes a generating function of the cubic Hodge integrals satisfying the Calabi-Yau condition, and claim that the whole family describes its generalization for the higher spin cases. To investigate this family we construct a new description of the Sato Grassmannian in terms of a canonical pair of the Kac-Schwarz operators.

arXiv comment83 pages, journal version

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• $x-y$ duality in Topological Recursion for exponential variables via Quantum Dilogarithm
• On higher Brézin-Gross-Witten tau-functions
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• KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions
• Cut-and-join operators in cohomological field theory and topological recursion
• The ordered exponential representation of GKM using the $W_{1+\infty }$ operator