Foliation of the Space \( \mathfrak{s}{\mathfrak{l}}^{\ast}\left(n,\mathbb{R}\right) \) into Coadjoint Orbits

Abstract

We suggest a method for constructing parameters on the coadjoint orbits in \( \mathfrak{s}{\mathfrak{l}}^{\ast}\left(n,\mathbb{R}\right) \). The method is based on the fact that parameters are invariant under the action of vector fields normal to the tangent space of the orbit with respect to the Killing form. The construction reduces to solving a homogeneous system of linear equations.