String-Orthogonal Polynomials, String equations, and 2-Toda symmetries

TL;DR

This paper explores the deep connections between string-orthogonal polynomials, the 2-Toda lattice, and associated symmetries, revealing new structures and constraints such as Virasoro conditions in matrix integrals.

Contribution

It introduces a novel framework linking string-orthogonal polynomials with the 2-Toda lattice and extends symmetry analysis to special initial conditions.

Findings

Identification of a larger symmetry class for specific initial conditions

Borel decomposition links moment matrices to tau-functions and polynomials

Derivation of Virasoro constraints on two-matrix integrals

Abstract

1. The 2-Toda lattice and its generic symmetries 2. A Larger class of symmetries for special initial conditions 3. Borel decomposition of Moment matrices, tau-functions and string-orthogonal polynomials 4. From string-orthogonal Polynomials to the 2-Toda lattice and the string equation 5. Virasoro constraints on two-matrix integrals