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Singular fibres of the Gelfand-Cetlin system on u(n)

Autor
Bouloc, D.; Miranda, E.; Tien Zung, N.
Tipus d'activitat
Article en revista
Revista
Philosophical transactions of the Royal Society A. Mathematical physical and engineering sciences
Data de publicació
2018-10-28
Volum
376
Número
2131
Pàgina inicial
423
Pàgina final
448
DOI
https://doi.org/10.1098/rsta.2017.0423 Obrir en finestra nova
Projecte finançador
Geometria de varietats i aplicacions (GEOMVAP)
Geometría y topología de variedades, algebra y aplicaciones
Repositori
http://hdl.handle.net/2117/122632 Obrir en finestra nova
URL
http://rsta.royalsocietypublishing.org/content/376/2131/20170423 Obrir en finestra nova
Resum
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 detaile...
Citació
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.
Paraules clau
Gelfand-Cetlin systems, Hamiltonian systems, Lagrangian fibres, integrable systems, singularities
Grup de recerca
GEOMVAP - Geometria de Varietats i Aplicacions

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