Loading...
Loading...

Go to the content (press return)

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

Author
Bouloc, D.; Miranda, E.; Tien Zung, N.
Type of activity
Journal article
Journal
Philosophical transactions of the Royal Society A. Mathematical physical and engineering sciences
Date of publication
2018-10-28
Volume
376
Number
2131
First page
423
Last page
448
DOI
https://doi.org/10.1098/rsta.2017.0423 Open in new window
Project funding
GEOMETRIA DE VRIETATS I APLICACIONS (GEOMVAP)
Geometry and topology of varieties, algebra and applications
Repository
http://hdl.handle.net/2117/122632 Open in new window
URL
http://rsta.royalsocietypublishing.org/content/376/2131/20170423 Open in new window
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 detaile...
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.
Keywords
Gelfand-Cetlin systems, Hamiltonian systems, Lagrangian fibres, integrable systems, singularities
Group of research
GEOMVAP - Geometry of Manifolds and Applications

Participants

Attachments