THE ALGEBRAIC GEOMETRY OF THE KOSTANT–KIRILLOV FORM
Large classes of integrable Hamiltonian systems can be expressed as systems over coadjoint orbits in a loop algebra defined over a semi-simple Lie algebra [gfr ]. These systems can then be integrated via the classical, symplectic Liouville–Arnold method. On the other hand, the existence of spectral...
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| Veröffentlicht in: | Journal of the London Mathematical Society 1997-12, Vol.56 (3), p.504-518 |
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| creator | HURTUBISE, J. C. |
| description | Large classes of integrable Hamiltonian systems can be expressed
as systems over coadjoint orbits in
a loop algebra defined over a semi-simple Lie algebra [gfr ].
These systems can then be integrated via the
classical, symplectic Liouville–Arnold method. On the other hand,
the existence of spectral curves as
constants of motion allows one to integrate these systems in terms of
flows of line bundles on the curves.
This note links the symplectic geometry of the coadjoint orbits with the
algebraic geometry of these curves
for arbitrary semi-simple [gfr ], which then allows us to reconcile the
two integration methods. |
| doi_str_mv | 10.1112/S0024610797005590 |
| format | Article |
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as systems over coadjoint orbits in
a loop algebra defined over a semi-simple Lie algebra [gfr ].
These systems can then be integrated via the
classical, symplectic Liouville–Arnold method. On the other hand,
the existence of spectral curves as
constants of motion allows one to integrate these systems in terms of
flows of line bundles on the curves.
This note links the symplectic geometry of the coadjoint orbits with the
algebraic geometry of these curves
for arbitrary semi-simple [gfr ], which then allows us to reconcile the
two integration methods.</description><identifier>ISSN: 0024-6107</identifier><identifier>EISSN: 1469-7750</identifier><identifier>DOI: 10.1112/S0024610797005590</identifier><language>eng</language><publisher>Cambridge University Press</publisher><subject>Notes and Papers</subject><ispartof>Journal of the London Mathematical Society, 1997-12, Vol.56 (3), p.504-518</ispartof><rights>The London Mathematical Society 1997</rights><rights>1997 London Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3734-34da8d529b1de09f9d6e5713704f965bb4483ae3bc6f61f46b9e67a1c255047b3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1112%2FS0024610797005590$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1112%2FS0024610797005590$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>HURTUBISE, J. C.</creatorcontrib><title>THE ALGEBRAIC GEOMETRY OF THE KOSTANT–KIRILLOV FORM</title><title>Journal of the London Mathematical Society</title><addtitle>J. Lond. Math. Soc</addtitle><description>Large classes of integrable Hamiltonian systems can be expressed
as systems over coadjoint orbits in
a loop algebra defined over a semi-simple Lie algebra [gfr ].
These systems can then be integrated via the
classical, symplectic Liouville–Arnold method. On the other hand,
the existence of spectral curves as
constants of motion allows one to integrate these systems in terms of
flows of line bundles on the curves.
This note links the symplectic geometry of the coadjoint orbits with the
algebraic geometry of these curves
for arbitrary semi-simple [gfr ], which then allows us to reconcile the
two integration methods.</description><subject>Notes and Papers</subject><issn>0024-6107</issn><issn>1469-7750</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1997</creationdate><recordtype>article</recordtype><recordid>eNqFkM1Og0AUhSdGE2v1AdzxAugd5q-zpA1QWiqG4u9mwsBgqK01oNHufAff0CcR0saNia7u4tzv3nMOQqcYzjDGzvkcwKEcg5ACgDEJe6iHKZe2EAz2Ua-T7U4_REdNswDABIPTQywde5YbBd4wccORFXjxzEuTOyv2rU6ZxvPUvUi_Pj6nYRJGUXxt-XEyO0YHZbZszMlu9tGV76WjsR3FQThyIzsnglCb0CIbFMyRGhcGZCkLbpjARAAtJWdaUzogmSE65yXHJeVaGi4ynDuMARWa9BHe3s3rddPUplTPdbXK6o3CoLrc6lfulhFb5q1ams3_gJpEszm0_1rS3pJV82Lef8isflRcEMHU-PZeXQZDeTNJJspv98nOXbbSdVU8GLVYv9ZPbSN_-PsGEeNztw</recordid><startdate>199712</startdate><enddate>199712</enddate><creator>HURTUBISE, J. C.</creator><general>Cambridge University Press</general><general>Oxford University Press</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>199712</creationdate><title>THE ALGEBRAIC GEOMETRY OF THE KOSTANT–KIRILLOV FORM</title><author>HURTUBISE, J. C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3734-34da8d529b1de09f9d6e5713704f965bb4483ae3bc6f61f46b9e67a1c255047b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1997</creationdate><topic>Notes and Papers</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>HURTUBISE, J. C.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>Journal of the London Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>HURTUBISE, J. C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>THE ALGEBRAIC GEOMETRY OF THE KOSTANT–KIRILLOV FORM</atitle><jtitle>Journal of the London Mathematical Society</jtitle><addtitle>J. Lond. Math. Soc</addtitle><date>1997-12</date><risdate>1997</risdate><volume>56</volume><issue>3</issue><spage>504</spage><epage>518</epage><pages>504-518</pages><issn>0024-6107</issn><eissn>1469-7750</eissn><abstract>Large classes of integrable Hamiltonian systems can be expressed
as systems over coadjoint orbits in
a loop algebra defined over a semi-simple Lie algebra [gfr ].
These systems can then be integrated via the
classical, symplectic Liouville–Arnold method. On the other hand,
the existence of spectral curves as
constants of motion allows one to integrate these systems in terms of
flows of line bundles on the curves.
This note links the symplectic geometry of the coadjoint orbits with the
algebraic geometry of these curves
for arbitrary semi-simple [gfr ], which then allows us to reconcile the
two integration methods.</abstract><pub>Cambridge University Press</pub><doi>10.1112/S0024610797005590</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0024-6107 |
| ispartof | Journal of the London Mathematical Society, 1997-12, Vol.56 (3), p.504-518 |
| issn | 0024-6107 1469-7750 |
| language | eng |
| recordid | cdi_crossref_primary_10_1112_S0024610797005590 |
| source | Wiley Online Library Journals Frontfile Complete; Alma/SFX Local Collection |
| subjects | Notes and Papers |
| title | THE ALGEBRAIC GEOMETRY OF THE KOSTANT–KIRILLOV FORM |
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