On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups

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On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups. / Babich, M. V.

In: Journal of Mathematical Sciences (United States), Vol. 209, No. 6, 2015, p. 830-844.

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Babich, M. V. / On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups. In: Journal of Mathematical Sciences (United States). 2015 ; Vol. 209, No. 6. pp. 830-844.

BibTeX

@article{3929b44e9aa34e3b8a6031f4e671c3f5,

title = "On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups",

abstract = "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 SONℂ and SpNℂ. 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 pk, qk on the orbit such that the symplectic form of the orbit is equal to (Formula Presented.). 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 A2. It contains the case of general position, the general diagonalizable case, and many others.",

keywords = "Symplectic Form, Orthogonal Group, Diagonal Block, symplectic group, General linear group",

author = "Babich, {M. V.}",

note = "Babich, M.V. On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups. J Math Sci 209, 830–844 (2015). https://doi.org/10.1007/s10958-015-2530-2",

year = "2015",

doi = "10.1007/s10958-015-2530-2",

language = "English",

volume = "209",

pages = "830--844",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "6",

}

RIS

TY - JOUR

T1 - On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups

AU - Babich, M. V.

N1 - Babich, M.V. On Birational Darboux Coordinates on Coadjoint Orbits of Classical Complex Lie Groups. J Math Sci 209, 830–844 (2015). https://doi.org/10.1007/s10958-015-2530-2

PY - 2015

Y1 - 2015

N2 - 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 SONℂ and SpNℂ. 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 pk, qk on the orbit such that the symplectic form of the orbit is equal to (Formula Presented.). 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 A2. It contains the case of general position, the general diagonalizable case, and many others.

AB - 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 SONℂ and SpNℂ. 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 pk, qk on the orbit such that the symplectic form of the orbit is equal to (Formula Presented.). 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 A2. It contains the case of general position, the general diagonalizable case, and many others.

KW - Symplectic Form

KW - Orthogonal Group

KW - Diagonal Block

KW - symplectic group

KW - General linear group

UR - http://www.scopus.com/inward/record.url?scp=84939435620&partnerID=8YFLogxK

U2 - 10.1007/s10958-015-2530-2

DO - 10.1007/s10958-015-2530-2

M3 - Article

AN - SCOPUS:84939435620

VL - 209

SP - 830

EP - 844

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 35280254