ИСТИНА

We prove that the full symmetric Toda system is integrable in the sense of the Lie-Bianchi criterion, i.e. that there exists a solvable Lie algebra of vector fields of dimension N = dim M on the phase space M of this system such that the system is invariant with respect to the action of these fields. The proof is based on the use of symmetries of the full symmetric system, which we described earlier (see paper 1.), and the appearance of the structure of the stochastic Lie algebra in their description. The talk is based on a joint paper with Yu.Chernyakov and D.Talalaev. REFERENCES 1. Sorin A.S., Chernyakov Yu.B., Sharygin G.I., “Vector fields and invariants of the full symmetric Toda system”, Theoret. and Math. Phys., 216, No. 2, 1142–1157 (2023)