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arXiv · 1905.08140

On tau-functions for the Toda lattice hierarchy

Di Yang
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Abstract

We extend a recent result of [13] for the KdV hierarchy to the Toda lattice hierarchy. Namely, for an arbitrary solution to the Toda lattice hierarchy, we define a pair of wave functions, and use them to give explicit formulae for the generating series of $k$-point correlation functions of the solution. Applications to computing GUE correlators and Gromov--Witten invariants of the Riemann sphere are under consideration.

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Di Yang. 2019-10-20. On tau-functions for the Toda lattice hierarchy. https://doi.org/10.1007/s11005-019-01232-5

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