On the invariants of the full symmetric Toda system

Autor:	Chernyakov, Yu. B., Sharygin, G. I, Sorin, A. S.
Rok vydání:	2019
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	In this paper we continue our study of the geometric properties of full symmetric Toda systems from \cite{CSS14,CSS17,CSS19}. Namely we describe here a simple geometric construction of a commutative family of vector fields on compact groups, that include the Toda vector field, i.e. the field, which generates the full symmetric Toda system associated with the Cartan decomposition of a semisimple Lie algebra. Our construction makes use of the representations of the semisimple algebra and does not depend on the splitness of the Cartan pair. It is very close to the family of invariants and semiinvariants of the Toda system associted with $SL_n$, introduced in \cite{CS}. Comment: 22 pages, 5 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1910.04789 Zobrazit plný text záznamu View this record from Arxiv