References around Gelfand-Cetlin

By ntzung, on March 14th, 2007

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 ?)

* Giacobbe: Some remarks on the Gelfand-Cetlin system, J. Phys. A 35 (2002), 10591-10605.

* 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.

* Alekseev & Meinrenken: Ginzburg-Weinstein via Gelfand-Cetlin, 2005 (from su(n)* to SU(n)*)

* Bielawski & Pydstrygach, Gelfand-Zeitlin actions and rational maps, 2006.