Vector fields and invariants of the full symmetric Toda system. (English. Russian original) Zbl 1521.37060
Theor. Math. Phys. 216, No. 2, 1142-1157 (2023); translation from Teor. Mat. Fiz. 216, No. 2, 271-290 (2023).
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 \(SL_n\).
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37J37 | Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures |
| 17B80 | Applications of Lie algebras and superalgebras to integrable systems |
Keywords:
full symmetric Toda system; commutative families of vector fields; Lie algebras representationsReferences:
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