Affine Weyl group symmetry of the Garnier system

2003/12/25 by Takao Suzuki, Suzuki, Takao
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Representation Theory (math.RT) #math-ph #math.MP #math.RT

paper · pdf · doi:10.48550/arxiv.math-ph/0312068

33 pages

openalex publication_date 2003/12/25 · arxiv created 2005/03/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Garnier system in n-variables has affine Weyl group symmetry of type B⁽¹⁾_n+3. We also formulate the τ functions for the Garnier system (or the Schlesinger system of rank 2) on the root lattice Q(C_n+3) and show that they satisfy Toda equations, Hirota-Miwa equations and bilinear differential equations.

Related

• Toda equation and special polynomials associated with the Garnier system
• Studies on the Garnier system in two variables
• The geometry of the classical solutions of the Garnier systems
• Ordinary differential systems in dimension three with affine Weyl group symmetry of types D₄⁽¹⁾,B₃⁽¹⁾,G₂⁽¹⁾,D₃⁽²⁾ and A₂⁽²⁾
• Symmetric Hamiltonian of the Garnier system and its degenerate systems in two variables