Configurations of points and the symplectic Berry-Robbins problem
We present a new problem on configurations of points, which is a new version of a similar problem by Atiyah and Sutcliffe, except it is related to the Lie group Sp(n), instead of the Lie group U(n). Denote by h a Cartan algebra of Sp(n), and Δ the union of the zero sets of the roots of Sp(n) tensore...
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| Дата: | 2014 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146322 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Configurations of points and the symplectic Berry-Robbins problem / J. Malkoun // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1463222019-02-09T01:25:03Z Configurations of points and the symplectic Berry-Robbins problem Malkoun, J. We present a new problem on configurations of points, which is a new version of a similar problem by Atiyah and Sutcliffe, except it is related to the Lie group Sp(n), instead of the Lie group U(n). Denote by h a Cartan algebra of Sp(n), and Δ the union of the zero sets of the roots of Sp(n) tensored with R3, each being a map from h⊗R3→R3. We wish to construct a map (h⊗R3)∖Δ→Sp(n)/Tn which is equivariant under the action of the Weyl group Wn of Sp(n) (the symplectic Berry-Robbins problem). Here, the target space is the flag manifold of Sp(n), and Tn is the diagonal n-torus. The existence of such a map was proved by Atiyah and Bielawski in a more general context. We present an explicit smooth candidate for such an equivariant map, which would be a genuine map provided a certain linear independence conjecture holds. We prove the linear independence conjecture for n=2. 2014 Article Configurations of points and the symplectic Berry-Robbins problem / J. Malkoun // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 5 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 51F99; 17B22 http://dspace.nbuv.gov.ua/handle/123456789/146322 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 |
We present a new problem on configurations of points, which is a new version of a similar problem by Atiyah and Sutcliffe, except it is related to the Lie group Sp(n), instead of the Lie group U(n). Denote by h a Cartan algebra of Sp(n), and Δ the union of the zero sets of the roots of Sp(n) tensored with R3, each being a map from h⊗R3→R3. We wish to construct a map (h⊗R3)∖Δ→Sp(n)/Tn which is equivariant under the action of the Weyl group Wn of Sp(n) (the symplectic Berry-Robbins problem). Here, the target space is the flag manifold of Sp(n), and Tn is the diagonal n-torus. The existence of such a map was proved by Atiyah and Bielawski in a more general context. We present an explicit smooth candidate for such an equivariant map, which would be a genuine map provided a certain linear independence conjecture holds. We prove the linear independence conjecture for n=2. |
| format |
Article |
| author |
Malkoun, J. |
| spellingShingle |
Malkoun, J. Configurations of points and the symplectic Berry-Robbins problem Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Malkoun, J. |
| author_sort |
Malkoun, J. |
| title |
Configurations of points and the symplectic Berry-Robbins problem |
| title_short |
Configurations of points and the symplectic Berry-Robbins problem |
| title_full |
Configurations of points and the symplectic Berry-Robbins problem |
| title_fullStr |
Configurations of points and the symplectic Berry-Robbins problem |
| title_full_unstemmed |
Configurations of points and the symplectic Berry-Robbins problem |
| title_sort |
configurations of points and the symplectic berry-robbins problem |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146322 |
| citation_txt |
Configurations of points and the symplectic Berry-Robbins problem / J. Malkoun // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 5 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT malkounj configurationsofpointsandthesymplecticberryrobbinsproblem |
| first_indexed |
2023-05-20T17:24:34Z |
| last_indexed |
2023-05-20T17:24:34Z |
| _version_ |
1796153227938365440 |