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Bruhat Order in the Full Symmetric $\mathfrak{sl}_n$ Toda Lattice on partial flag spacesстатья
- Авторы: Сорин А.С., Черняков Ю.Б., Шарыгин Г.И.
- Журнал: Symmetry, Integrability and Geometry - Methods and Applications
- Том: 12
- Номер: 084
- Год издания: 2016
- Издательство: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
- Местоположение издательства: Ukraine
- DOI: 10.3842/SIGMA.2016.084
- Аннотация: In our previous paper [Comm. Math. Phys. 330 (2014), 367-399] we described the asymptotic behaviour of trajectories of the full symmetric sl_n Toda lattice in the case of distinct eigenvalues of the Lax matrix. It turned out that it is completely determined by the Bruhat order on the permutation group. In the present paper we extend this result to the case when some eigenvalues of the Lax matrix coincide. In that case the trajectories are described in terms of the projection to a partial flag space where the induced dynamical system verifies the same properties as before: we show that when t→±∞ the trajectories of the induced dynamical system converge to a finite set of points in the partial flag space indexed by the Schubert cells so that any two points of this set are connected by a trajectory if and only if the corresponding cells are adjacent. This relation can be explained in terms of the Bruhat order on multiset permutations.
- Добавил в систему: Шарыгин Георгий Игорьевич