17 citations · 43 across the 13 of their papers we have counts for
14 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 and vector fields on the group
Yu. B. Chernyakov, G. I. Sharygin
In this paper we discuss the relation between the functions that give first integrals of full symmetric Toda system (an important Hamilton system on the space of traceless real sym…
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…
A fully noncommutative analog of the Painlevé IV equation and a structure of its solutions
Irina Bobrova, Vladimir Retakh, Vladimir Rubtsov +1
We study a fully noncommutative generalisation of the commutative fourth Painlevé equation that possesses solutions in terms of an infinite Toda system over an associative unital d…
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…
Noncommutative cross-ratio and Schwarz derivative
Vladimir Retakh, Vladimir Rubtsov, Georgy Sharygin
We present here a theory of noncommutative cross-ratio, Schwarz derivative and their connections and relations to the operator cross-ratio. We apply the theory to "noncommutative e…
The Full Symmetric Toda Flow and Intersections of Bruhat Cells
Yuri B. Chernyakov, Georgy I. Sharygin, Alexander S. Sorin +1
In this short note we show that the Bruhat cells in real normal forms of semisimple Lie algebras enjoy the same property as their complex analogs: for any two elements , in…
On local combinatorial formulas for Chern classes of triangulated circle bundle
Nikolai Mnev, Georgy Sharygin
Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To…
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…
Cohomology of the tetrahedral complex and quasi-invariants of 2-knots
I. G. Korepanov, G. I. Sharygin, D. V. Talalaev
This paper explores a particular statistical model on 6-valent graphs with special properties which turns out to be invariant with respect to certain Roseman moves if the graph is…
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…
Cohomologies of -simplex relations
Igor Korepanov, Georgy Sharygin, Dmitry Talalaev
A theory of (co)homologies related to set-theoretic -simplex relations is constructed in analogy with the known quandle and Yang--Baxter (co)homologies, with emphasis made on th…
Bruhat Order in Full Symmetric Toda System
Yu. B. Chernyakov, G. I. Sharygin, A. S. Sorin
In this paper we discuss some geometrical and topological properties of the full symmetric Toda system. We show by a direct inspection that the phase transition diagram for the ful…
Deformation quantization of integrable systems
Georgy Sharygin, Dmitry Talalaev
In this paper we address the following question: is it always possible to choose a deformation quantization of a Poisson algebra A so that certain Poisson-commutative subalgebra C…