I’m collecting in this page references directly related to the Gelfand-Cetlin system.
The list is ordered chronologically.
* Gelfand & Cetlin ? (around 1950)
* Thimm: Integrable geodesic flows on homology spheres, Ergodic Th. Dyn. Syst. 1 (1981), 595–517. (the first paper in which the integrable GC system appears ?)
* Guillemin & Sternberg: The Gelfand-Cetlin system and quantization of the complex flag manifolds, J. Funct. Anal. 52 (1983)
* Guillemin & Sternberg:
* Hausmann & Knutson: Polygon spaces and Grassmannians, l’Enseignement Math. 43 (1997), 173–198. (This paper shows a kind of isomorphism of the GC system on a regular coadjoint orbit with the bending flow in the space of polygons ?)
* Kostant & Wallach: Gelfand-Zeitlin theory from the perspective of classical mechanics, I, 2004.
* Kostant & Wallach: Gelfand-Zeitlin theory from the perspective of classical mechanics, II, 2005.