Toda equation and special polynomials associated with the Garnier system

2004/08/31 by Teruhisa Tsuda, Tsuda, Teruhisa
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0408060

26 pages

arxiv created 2004/08/31 · openalex publication_date 2004/08/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a certain sequence of tau functions of the Garnier system satisfies Toda equation. We construct a class of algebraic solutions of the system by the use of Toda equation; then show that the associated tau functions are expressed in terms of the universal character, which is a generalization of Schur polynomial attached to a pair of partitions.

Related

• Affine Weyl group symmetry of the Garnier system
• Classical solutions of the degenerate Garnier system and their coalescence structures
• d-orthogonal polynomials, Toda Lattice and Virasoro symmetries
• The geometry of the classical solutions of the Garnier systems
• Diagonal Solutions to the 2-Toda Hierarchy