arXiv subjects
Publications and source records attributed to Guillaume Deltour.
Let G be a simple, noncompact, connected, real Lie group with finite center, and K a maximal compact subgroup of G. We assume that G/K is Hermitian. Using GIT methods derived from the generalized eigenvalue problem, we compute a set of affine equations describing the moment polyhedron of the projection on k* of holomorphic coadjoint orbits of G.
We study the symplectic structure of the holomorphic coadjoint orbits, generalizing a theorem of McDuff on the symplectic structure of Hermitian symmetric spaces of noncompact type.
This thesis studies the symplectic structure of holomorphic coadjoint orbits, and their projections. A holomorphic coadjoint orbit O is an elliptic coadjoint orbit which is endowed with a natural invariant Kählerian structure. These coadjoint orbits are defined for a real semi-simple connected non-compact Lie group G with finite center, such that G/K is a Hermitian symmetric space, where K is a maximal compact subgroup of G. Holomorphic coadjoint orbits are a generalization of the Hermitian symmetric space G/K. In this thesis, we prove that the McDuff's symplectomorphism on Hermitian symmetric spaces, has an analogous for holomorphic coadjoint orbits. Then, using this symplectomorphism and recent GIT arguments from Ressayre, we compute the equations of the projection of the O, relatively to the maximal compact subgroup K.