Isotropic foliations of coadjoint orbits from the Iwasawa decomposition

Details Isotropic foliations of coadjoint orbits from the Iwasawa decomposition Isotropic foliations of coadjoint orbits from the Iwasawa decomposition

2009-11-16

arxiv.org/abs/0911.3039v2

Mathematics

Symplectic Geometry

15 pages; exposition shortened, typos corrected and errors corrected

Scientific paper

Let G be a noncompact real semisimple Lie group. The regular coadjoint orbits of G can be partitioned into a finite set of types. We show that on each regular orbit, the Iwasawa decomposition induces a left-invariant foliation which is isotropic with respect to the Kirillov symplectic form. Moreover, the leaves are affine subspaces of the dual of the Lie algebra, and the dimension of the leaves depends only on the type of the orbit. When G is a split real form, the foliations induced from the Iwasawa decomposition are actually Lagrangian fibrations with a global transverse Lagrangian section.

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