The symplectic and twister geometry of the general isomonodromic deformation problem
Hitchin's twistor treatment of Schlesinger's equations is extended to the general isomonodromic deformation problem. It is shown that a generic linear system of ordinary differential equations with gauge group SL(n,C) on a Riemann surface X can be obtained by embedding X in a twistor space...
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| Formatua: | Journal article |
| Hizkuntza: | English |
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2001
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| _version_ | 1826278475171889152 |
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| author | Woodhouse, N |
| author_facet | Woodhouse, N |
| author_sort | Woodhouse, N |
| collection | OXFORD |
| description | Hitchin's twistor treatment of Schlesinger's equations is extended to the general isomonodromic deformation problem. It is shown that a generic linear system of ordinary differential equations with gauge group SL(n,C) on a Riemann surface X can be obtained by embedding X in a twistor space Z on which sl(n,C) acts. When a certain obstruction vanishes, the isomonodromic deformations are given by deforming X in Z. This is related to a description of the deformations in terms of Hamiltonian flows on a symplectic manifold constructed from affine orbits in the dual Lie algebra of a loop group. © 2001 Elsevier Science B.V. |
| first_indexed | 2024-03-06T23:44:28Z |
| format | Journal article |
| id | oxford-uuid:706b91e5-5100-43da-b75f-b7180bb67d9e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:44:28Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:706b91e5-5100-43da-b75f-b7180bb67d9e2022-03-26T19:37:05ZThe symplectic and twister geometry of the general isomonodromic deformation problemJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:706b91e5-5100-43da-b75f-b7180bb67d9eEnglishSymplectic Elements at Oxford2001Woodhouse, NHitchin's twistor treatment of Schlesinger's equations is extended to the general isomonodromic deformation problem. It is shown that a generic linear system of ordinary differential equations with gauge group SL(n,C) on a Riemann surface X can be obtained by embedding X in a twistor space Z on which sl(n,C) acts. When a certain obstruction vanishes, the isomonodromic deformations are given by deforming X in Z. This is related to a description of the deformations in terms of Hamiltonian flows on a symplectic manifold constructed from affine orbits in the dual Lie algebra of a loop group. © 2001 Elsevier Science B.V. |
| spellingShingle | Woodhouse, N The symplectic and twister geometry of the general isomonodromic deformation problem |
| title | The symplectic and twister geometry of the general isomonodromic deformation problem |
| title_full | The symplectic and twister geometry of the general isomonodromic deformation problem |
| title_fullStr | The symplectic and twister geometry of the general isomonodromic deformation problem |
| title_full_unstemmed | The symplectic and twister geometry of the general isomonodromic deformation problem |
| title_short | The symplectic and twister geometry of the general isomonodromic deformation problem |
| title_sort | symplectic and twister geometry of the general isomonodromic deformation problem |
| work_keys_str_mv | AT woodhousen thesymplecticandtwistergeometryofthegeneralisomonodromicdeformationproblem AT woodhousen symplecticandtwistergeometryofthegeneralisomonodromicdeformationproblem |