On tau-functions for the Toda lattice hierarchy

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.

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

References in corpus (8)

• 2D Gravity and Random Matrices
• The Topological CP^1 Model and the Large-N Matrix Integral
• D-particles, Matrix Integrals and KP hierachy
• The Extended Bigraded Toda hierarchy
• Virasoro Symmetries of the Extended Toda Hierarchy
• Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$
• Generating series for GUE correlators
• WKB solutions of difference equations and reconstruction by the topological recursion

Cited by in corpus (4)

• Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials
• Matrix resolvent and the discrete KdV hierarchy
• Grothendieck's Dessins d'Enfants in a Web of Dualities. III
• Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method