On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2530-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2530-2 | ||
| 100 | 1 | |a Babich |D M. |u St.Petersburg Department of Steklov Mathematical Institute, St.Petersburg State University, St.Petersburg, Russia |4 aut | |
| 245 | 1 | 0 | |a On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups |h [Elektronische Daten] |c [M. Babich] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 209/6(2015-09-01), 830-844 |x 1072-3374 |q 209:6<830 |1 2015 |2 209 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2530-2 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2530-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Babich |D M. |u St.Petersburg Department of Steklov Mathematical Institute, St.Petersburg State University, St.Petersburg, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 209/6(2015-09-01), 830-844 |x 1072-3374 |q 209:6<830 |1 2015 |2 209 |o 10958 | ||