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The paper is devoted to the algebraic and geometric aspects of the fullsymmetric Toda system. We construct a solution to the completeDeift-Li-Nanda-Tomei flows system using the QR decomposition method. For thispurpose we introduce specialized invariant tensor operations on the Laxoperator of the model. These operations have a direct interpretation in termsof the representation theory of Lie algebras. We expect that this approach canbe effective in studying the geometry of flag varieties.

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