28 citations · 58 across the 10 of their papers we have counts for
10 papers
The Lie -Bianchi integrability of the full symmetric Toda system
Yury B. Chernyakov, Georgy I. Sharygin, Dmitry V. Talalaev
In this paper 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 o…
Full symmetric Toda system: QR-solution for complete DLNT-family
Yury B. Chernyakov, Georgy I. Sharygin, Dmitry V. Talalaev
The paper is devoted to the algebraic and geometric aspects of the full symmetric Toda system. We construct a solution to the complete Deift-Li-Nanda-Tomei flows system using the Q…
On the invariants of the full symmetric Toda system
Yu. B. Chernyakov, G. I Sharygin, A. S. Sorin
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 constructio…
Bruhat order in the Toda system on : an example of non-split real form
Yu. B. Chernyakov, G. I. Sharygin, A. S. Sorin
In our previous papers we described the structure of trajectories of the symmetric Toda system on normal real forms of various Lie algebras and showed that it was totally determine…
Phase portraits of the generalized full symmetric Toda systems on rank 2 groups
Yu. B. Chernyakov, G. I Sharygin, A. S. Sorin
In this paper we continue investigations that we began in our previous works, where we proved, that the phase diagram of Toda system on special linear groups can be identified with…
Bruhat Order in the Full Symmetric Toda Lattice on Partial Flag Space
Yury B. Chernyakov, Georgy I. Sharygin, Alexander S. Sorin
In our previous paper [Comm. Math. Phys. 330 (2014), 367-399] we described the asymptotic behaviour of trajectories of the full symmetric Toda lattice in the case…
Semi-invariants and Integrals of the Full Symmetric sl(n) Toda Lattice
Yu. B. Chernyakov, A. S. Sorin
We consider the full symmetric version of the Lax operator of the Toda lattice which is known as the full symmetric Toda lattice. The phase space of this system is the generic orbi…
Explicit Semi-invariants and Integrals of the Full Symmetric sl(n) Toda Lattice
Yu. B. Chernyakov, A. S. Sorin
We show how to construct semi-invariants and integrals of the full symmetric sl(n) Toda lattice for all n. Using the Toda equations for the Lax eigenvector matrix we prove the exis…
Quadratic algebras related to elliptic curves
Yu. Chernyakov, A. M. Levin, M. Olshanetsky +1
We construct quadratic finite-dimensional Poisson algebras and their quantum versions related to rank N and degree one vector bundles over elliptic curves with n marked points. The…
Elliptic Schlesinger system and Painlev{é} VI
Yu. Chernyakov, A. M. Levin, M. Olshanetsky +1
We construct an elliptic generalization of the Schlesinger system (ESS) with positions of marked points on an elliptic curve and its modular parameter as independent variables (the…