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Full symmetric Toda system: QR-solution for complete DLNT-family
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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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Cited by 2 Pith papers
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The Lie -Bianchi integrability of the full symmetric Toda system
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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Full symmetric Toda system and vector fields on the group $SO_n(\R)$
For B^+_n(R)-invariant functions f and g on sl_n(R), the associated vector fields T_f and T_g on SO_n(R) satisfy [T_f, T_g] = T_{f,g}, so f maps to T_f as a Lie algebra homomorphism.
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