Symmetries of the Full Symmetric Toda Flow
Time: 2022-11-07
Published By: Wenqiong Li
Speaker(s): Georgy Igorevich Sharygin (Moscow State University)
Time: 14:00-15:00 November 15, 2022
Venue: Room 29, Quan Zhai, BICMR
The full symmetric Toda flow is a rather straightforward generalisation of the standard "three-diagonal" Toda system: instead of the three-diagonal symmetric matrix one just considers the same equation for a general symmetric matrices. This system turns out to be integrable (i.e. it is a Hamiltonian system and has a sufficiently large number of first integrals in involution). In my talk I will describe a construction that gives large family of vector fields, that commute with Toda system, independently of the first integrals. The relation of this construction and the known constructions of the first integrals of the system is yet to be described.
