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Singular fibres of the Gelfand-Cetlin system on u(n)
dc.contributor.author | Bouloc, Damien |
dc.contributor.author | Miranda Galcerán, Eva |
dc.contributor.author | Tien Zung, Nguyen |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2018-10-18T14:42:15Z |
dc.date.available | 2018-10-18T14:42:15Z |
dc.date.issued | 2018-10-28 |
dc.identifier.citation | Bouloc, D., Miranda, E., Tien Zung, N. Singular fibres of the Gelfand-Cetlin system on u(n). "Philosophical transactions of the Royal Society A. Mathematical physical and engineering sciences", 28 Octubre 2018, vol. 376, núm. 2131, p. 423-448. |
dc.identifier.issn | 1364-503X |
dc.identifier.uri | http://hdl.handle.net/2117/122632 |
dc.description.abstract | In this paper, we show that every singular fibre of the Gelfand–Cetlin system on co-adjoint orbits of unitary groups is a smooth isotropic submanifold which is diffeomorphic to a two-stage quotient of a compact Lie group by free actions of two other compact Lie groups. In many cases, these singular fibres can be shown to be homogeneous spaces or even diffeomorphic to compact Lie groups. We also give a combinatorial formula for computing the dimensions of all singular fibres, and give a detailed description of these singular fibres in many cases, including the so-called (multi-)diamond singularities. These (multi-)diamond singular fibres are degenerate for the Gelfand–Cetlin system, but they are Lagrangian submanifolds diffeomorphic to direct products of special unitary groups and tori. Our methods of study are based on different ideas involving complex ellipsoids, Lie groupoids and also general ideas coming from the theory of singularities of integrable Hamiltonian systems |
dc.format.extent | 26 p. |
dc.language.iso | eng |
dc.publisher | Royal Society |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
dc.subject.lcsh | Topological manifolds |
dc.subject.other | integrable systems |
dc.subject.other | Gelfand-Cetlin systems |
dc.subject.other | singularities |
dc.subject.other | Lagrangian fibres |
dc.subject.other | Hamiltonian systems |
dc.title | Singular fibres of the Gelfand-Cetlin system on u(n) |
dc.type | Article |
dc.subject.lemac | Varietats topològiques |
dc.contributor.group | Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
dc.identifier.doi | 10.1098/rsta.2017.0423 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | http://rsta.royalsocietypublishing.org/content/376/2131/20170423 |
dc.rights.access | Open Access |
local.identifier.drac | 23358626 |
dc.description.version | Preprint |
local.citation.author | Bouloc, D.; Miranda, E.; Tien Zung, N. |
local.citation.publicationName | Philosophical transactions of the Royal Society A. Mathematical physical and engineering sciences |
local.citation.volume | 376 |
local.citation.number | 2131 |
local.citation.startingPage | 423 |
local.citation.endingPage | 448 |
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