Totally real orbits in affine quotients of reductive groups

Abstract

Let K be a compact connected Lie group and L a closed subgroup of K In [8] M. Lassalle proves that if K is semisimple and L is a symmetric subgroup of K c c then the holomorphy hull of any ϋC-invariant domain in K /L contains K/L. In

Homogeneous Lagrangian submanifolds

“…Here there are more than one K-Lagrangian orbit but, moving through points exp itZp, one does not meet any (other) Lagrangian orbit. Azad, Loeb and Qureshi [3] give necessary and sufficient conditions under which one can prove that there are infinitely many totally real orbits; more precisely this is the case whenever N G (G p )/G p is not finite. In the non-semisimple case this condition is always satisfied.…”

Hamiltonian actions and homogeneous Lagrangian submanifolds

“…It is well-known, shrinking the neighborhood of the zero section of (1). This claims that the dimension of the moduli space of Lagrangian orbits which contains Gx (1). We also deduce that Gx is isolated if and only if z(g) ∩ s = {0} if and only if the projection of g into g x maps z(g) one-to-one to z(g x ).…”

“…We recall that we may split g = g x ⊕ m as G x -modules and j is induced by the above decomposition, see [2]. It is well-known, shrinking the neighborhood of the zero section of (1). This claims that the dimension of the moduli space of Lagrangian orbits which contains Gx (1).…”