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Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space
Інший ID:
2010 Mathematics Subject Classification: 06A06; 37D15; 37J35
DOI:10.3842/SIGMA.2016.084
DOI:10.3842/SIGMA.2016.084
Посилання:
Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space
/ Y.B. Chernyakov, G.I. Sharygin, A.S. Sorin // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 23 назв. — англ.
Підтримка:
The authors would like to thank G. Koshevoy for the fruitful discussion. We also would like to
thank the referees, whose remarks helped in a great measure to improve the paper. The work
of Yu.B. Chernyakov was supported by grant RFBR-15-01-08462. The work of G.I. Sharygin
was supported by grant RFBR-15-01-05990. The work of A.S. Sorin was partially supported by
RFBR grants 15-52-05022-Arm-a and 16-52-12012-NNIO-a.
Дата:
2016
Переглядів:
532
Завантажень:
233
Анотація:
In our previous paper [Comm. Math. Phys. 330 (2014), 367-399] we described the asymptotic behaviour of trajectories of the full symmetric sln 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.
