Action integrals along closed isotopies in coadjoint orbits

Details Action integrals along closed isotopies in coadjoint orbits Action integrals along closed isotopies in coadjoint orbits

2001-03-26

arxiv.org/abs/math/0103161v1

Mathematics

Symplectic Geometry

12 pages, Latex

Scientific paper

Let ${\cal O}$ be the orbit of $\eta\in{\frak g}^*$ under the coadjoint action of the compact Lie group $G$. We give two formulae for calculating the action integral along a closed Hamiltonian isotopy on ${\cal O}$. The first one expresses this action in terms of a particular character of the isotropy subgroup of $\eta$. In the second one is involved the character of an irreducible representation of $G$.

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