paper

On tau-functions for the Toda lattice hierarchy

arXiv:1905.08140 · doi:10.1007/s11005-019-01232-5

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 -point correlation functions of the solution. Applications to computing GUE correlators and Gromov--Witten invariants of the Riemann sphere are under consideration.

added Appendix A on abstract wave functions, added references; 24 pages

On tau-functions for the Toda lattice hierarchy · wovepaper