Vector fields and invariants of the full symmetric Toda system

The geometric properties of the full symmetric Toda systems are studied. A simple geometric construction is described that allows constructing a commutative family of vector fields on a compact group including the Toda vector field, i.e., the field that generates the full symmetric Toda system assoc...

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Bibliographic Details
Published in:Theoretical and mathematical physics 2023-08, Vol.216 (2), p.1142-1157
Main Authors: Sorin, A. S., Chernyakov, Yu. B., Sharygin, G. I.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Applications of Mathematics
Fields (mathematics)
Invariants
Lie groups
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
Vectors (mathematics)
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Summary:The geometric properties of the full symmetric Toda systems are studied. A simple geometric construction is described that allows constructing a commutative family of vector fields on a compact group including the Toda vector field, i.e., the field that generates the full symmetric Toda system associated with the Cartan decomposition of a semisimple Lie algebra. Our construction involves representations of a semisimple algebra and is independent of whether the Cartan pair is split. The result is closely related to the family of invariants and semiinvariants for the Toda system on .
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577923080068