Full symmetric Toda system: QR-solution for complete DLNT-family
Yury B. Chernyakov, Georgy I. Sharygin, Dmitry V. Talalaev
TL;DR
This paper develops a QR-decomposition based solution for the full symmetric Toda system, linking algebraic, geometric, and Lie algebra representation theory aspects to study the system's integrability and geometric structure.
Contribution
It introduces a novel QR-based solution method for the complete DLNT-family of Toda systems using invariant tensor operations related to Lie algebra representations.
Findings
Constructed explicit QR-solution for the full symmetric Toda system.
Connected tensor operations to Lie algebra representation theory.
Potential applications in studying the geometry of flag varieties.
Abstract
The paper is devoted to the algebraic and geometric aspects of the full symmetric Toda system. We construct a solution to the complete Deift-Li-Nanda-Tomei flows system using the QR decomposition method. For this purpose we introduce specialized invariant tensor operations on the Lax operator of the model. These operations have a direct interpretation in terms of the representation theory of Lie algebras. We expect that this approach can be effective in studying the geometry of flag varieties.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra