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

@inproceedings{Alexandrov2021KPIO, title={KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions}, author={Alexander Alexandrov}, year={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 of the Heisenberg–Virasoro constraints. We also construct several equivalent versions of the cut-and-join operators. These operators describe the algebraic version of topological recursion. For the specific values of parameters associated with the KdV reduction, we prove that these tau-functions are…

## 2 Citations

Cut-and-join operators for higher Weil-Petersson volumes

- Mathematics, Physics
- 2021

In this paper, we construct the cut-and-join operator description for the generating functions of all intersection numbers of ψ, κ, and Θ classes on the moduli spaces Mg,n. The cut-and-join operators…

On the Hodge-BGW correspondence

- Mathematics, Physics
- 2021

We establish an explicit relationship between the partition function of certain special cubic Hodge integrals and the generalized Brézin–Gross–Witten (BGW) partition function, which we refer to as…

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