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Bruhat Order in the Full Symmetric $\mathfrak{sl}_n$ Toda Lattice on partial flag spaceстатья Электронная публикация
- Авторы: Chernyakov Yu B., Sharygin G.I., Sorin A.S.
- Сборник: ArXiv e-prints
- Серия: 1402.5747
- Том: 7464
- Год издания: 2014
- Место издания: ArXiv e-prints
- Аннотация: In our previous paper we described the asymptotic behaviour of trajectories of the Full Symmetric ��������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 generic case: let some eigenvalues of the Lax matrix coincide. In that case the trajectories are described in the 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 iff the corresponding cells are adjoint.
- Добавил в систему: Шарыгин Георгий Игорьевич