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pro vyhledávání: '"Chernyakov, Yu."'
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 inc
Externí odkaz:
http://arxiv.org/abs/1910.04789
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 determined by the Hasse diagram of the Bruhat order on the corresponding Weil g
Externí odkaz:
http://arxiv.org/abs/1712.09138
Autor:
Sorin, A. S.1,2,3 (AUTHOR), Chernyakov, Yu. B.4,5,6 (AUTHOR) chernyakov@itep.ru, Sharygin, G. I.4,5,7 (AUTHOR)
Publikováno v:
Theoretical & Mathematical Physics. Aug2023, Vol. 216 Issue 2, p1142-1157. 16p.
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 the Bruhat order on symmetric group, when all the eigenvalues of Lax
Externí odkaz:
http://arxiv.org/abs/1512.05821
Akademický článek
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Autor:
Chernyakov, Yu. B., Sorin, A. S.
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 orbit of the coadjoint action of the Borel subgroup B^+(n) of SL(n,R). Thi
Externí odkaz:
http://arxiv.org/abs/1312.4555
Autor:
Chernyakov, Yu. B., Sorin, A. S.
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 existence of semi-invariants which are homogeneous coordinates in the corr
Externí odkaz:
http://arxiv.org/abs/1306.1647
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 full symmetric Toda system in dimensions $n=3,4$ coincides with the Hasse
Externí odkaz:
http://arxiv.org/abs/1212.4803
Autor:
Chernyakov, Yu.
Using the point fusion procedure we obtain the new integrable systems from the Elliptic Schlesinger system (ESS). These new systems have the pole orders higher than one in the matrix of the Lax operator. Quadratic Poisson algebras on the phase space
Externí odkaz:
http://arxiv.org/abs/0812.4786
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 algebras are parameterized by the moduli of curves. For N=2 and n=1 t
Externí odkaz:
http://arxiv.org/abs/0710.1072