Configurations of points and the symplectic Berry-Robbins problem
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Configurations of points and the symplectic Berry-Robbins problem
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| Creator |
Malkoun, J.
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| 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.
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| Date |
2019-02-08T20:54:30Z
2019-02-08T20:54:30Z 2014 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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