Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space
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 grou...
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| Дата: | 2016 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147851 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1478512019-02-17T01:27:21Z Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space Chernyakov, Y.B. Sharygin, G.I. Sorin, A.S. 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. 2016 Article 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. 1815-0659 2010 Mathematics Subject Classification: 06A06; 37D15; 37J35 DOI:10.3842/SIGMA.2016.084 http://dspace.nbuv.gov.ua/handle/123456789/147851 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Chernyakov, Y.B. Sharygin, G.I. Sorin, A.S. |
| spellingShingle |
Chernyakov, Y.B. Sharygin, G.I. Sorin, A.S. Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Chernyakov, Y.B. Sharygin, G.I. Sorin, A.S. |
| author_sort |
Chernyakov, Y.B. |
| title |
Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space |
| title_short |
Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space |
| title_full |
Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space |
| title_fullStr |
Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space |
| title_full_unstemmed |
Bruhat Order in the Full Symmetric sln Toda Lattice on Partial Flag Space |
| title_sort |
bruhat order in the full symmetric sln toda lattice on partial flag space |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147851 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT chernyakovyb bruhatorderinthefullsymmetricslntodalatticeonpartialflagspace AT sharygingi bruhatorderinthefullsymmetricslntodalatticeonpartialflagspace AT sorinas bruhatorderinthefullsymmetricslntodalatticeonpartialflagspace |
| first_indexed |
2023-05-20T17:28:40Z |
| last_indexed |
2023-05-20T17:28:40Z |
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1796153386350936064 |