On Parametrization of the Symplectic Quotient of the Cartesian Product of Coadjoint Orbits of the Complex General Linear Group with Respect to its Diagonal Action

Abstract

We consider the problem of coordinatizing the manifold constructed via the Marsden–Weinstein quotient. Rational canonical coordinates on the symplectic reduction with respect to the diagonal action of the general linear group on the Cartesian product of coadjoint orbits in the case of the complex general linear group are constructed on an algebraically open subset of the quotient space. The method is based on an iterative process of constructing projection-flag coordinates, and works if the matrices constituting the orbits have a sufficiently rich set of invariant subspaces.