caa a22 4500 605525854 CHVBK 20210128100800.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10958-015-2530-2 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2530-2 Babich M. St.Petersburg Department of Steklov Mathematical Institute, St.Petersburg State University, St.Petersburg, Russia aut On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups [Elektronische Daten] [M. Babich] Any coadjoint orbit of the general linear group can be canonically parameterized using an iteration method, where at each step we turn from the matrix of a transformation A to the matrix of the transformation that is the projection of A parallel to an eigenspace of this transformation to a coordinate subspace. We present a modification of the method applicable to the groups SO N ℂ $$ \mathrm{SO}\left(N,\mathrm{\mathbb{C}}\right) $$ and S p N ℂ $$ \mathrm{S}\mathrm{p}\left(N,\mathrm{\mathbb{C}}\right) $$ . One step of the iteration consists of two actions, namely, the projection parallel to a subspace of an eigenspace and the simultaneous restriction to a subspace containing a co-eigenspace. The iteration gives a set of couples of functions p k , q k on the orbit such that the symplectic form of the orbit is equal to ∑ k d p k ^ d q k $$ {\displaystyle \sum_kd{p}_k\hat{\mkern6mu} d{q}_k} $$ . No restrictions on the Jordan form of the matrices forming the orbit are imposed. A coordinate set of functions is selected in the important case of the absence of nontrivial Jordan blocks corresponding to the zero eigenvalue, which is the case dim ker A = dim ker A 2. It contains the case of general position, the general diagonalizable case, and many others. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/6(2015-09-01), 830-844 1072-3374 209:6<830 2015 209 10958 https://doi.org/10.1007/s10958-015-2530-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2530-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Babich M. St.Petersburg Department of Steklov Mathematical Institute, St.Petersburg State University, St.Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/6(2015-09-01), 830-844 1072-3374 209:6<830 2015 209 10958