Infinite-dimensional hyperkaehler manifolds associated with Hermitian-symmetric affine coadjoint orbits

Details Infinite-dimensional hyperkaehler manifolds associated with Hermitian-symmetric affine coadjoint orbits Infinite-dimensional hyperkaehler manifolds associated with Hermitian-symmetric affine coadjoint orbits

2006-05-09

arxiv.org/abs/math-ph/0605032v2

Physics

Mathematical Physics

20 pages, 1 figure

Scientific paper

This paper is devoted to the construction of a hyperkaehler structure on the complexification of any Hermitian-symmetric affine coadjoint orbit O of a semi-simple L*-group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kaehler structure of O. By the identification of the complexification of O with the cotangent space of O induced by Mostow's Decomposition Theorem, this leads to the existence of a hyperkaehler structure on the cotangent space of O compatible with Liouville's symplectic form and whose restriction to the zero section is the Kaehler structure of O. Explicit formulas of the metric in terms of the complexified orbit and of the cotangent space are given.

Affiliated with

Also associated with

No associations

Rating

Infinite-dimensional hyperkaehler manifolds associated with Hermitian-symmetric affine coadjoint orbits does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Infinite-dimensional hyperkaehler manifolds associated with Hermitian-symmetric affine coadjoint orbits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinite-dimensional hyperkaehler manifolds associated with Hermitian-symmetric affine coadjoint orbits will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-675834