Geodesic
Vector fields and invariants of the~full symmetric Toda system
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 271-290

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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 $SL_n$.
Keywords: full symmetric Toda system, commutative families of vector fields, Lie algebras representations. 
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     author = {A. S. Sorin and Yu. B. Chernyakov and G. I. Sharygin},
     title = {Vector fields and invariants of the~full symmetric {Toda} system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {271--290},
     publisher = {mathdoc},
     volume = {216},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a5/}
}
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A. S. Sorin; Yu. B. Chernyakov; G. I. Sharygin. Vector fields and invariants of the~full symmetric Toda system. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 271-290. http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a5/