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Full symmetric Toda system: QR-solution for complete DLNT-family

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arxiv 2212.09148 v1 pith:2NDRVLTX submitted 2022-12-18 nlin.SI hep-thmath-phmath.MP

Yury B. Chernyakov , Georgy I. Sharygin , Dmitry V. Talalaev This is my paper
classification nlin.SIhep-thmath-phmath.MP
keywords systemcompletefulloperationssymmetrictodaalgebraicalgebras
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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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  1. The Lie -Bianchi integrability of the full symmetric Toda system

    nlin.SI 2025-06 reject novelty 6.0 of 10

    The paper identifies the Toda symmetry algebra with a central extension of the stochastic Lie algebra, but the claimed Lie-Bianchi integrability on the full phase space is not established.

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