String moduli spaces and parabolic factorizations

The symmetric spaces that appear as moduli spaces in string theory and supergravity can be decomposed with explicit metrics using parabolic subgroups. The resulting isometry between the original moduli space and this decomposition can be used to find parametrizations of the moduli. One application is to determine the volume parameter in conformal field moduli spaces for K3 surfaces. Other applications involve simple Dynkin diagram manipulations inducing “going up and down” between symmetric spaces by adding parameters and going to limits respectively. For supersymmetries such as N = 6, this involves combinatorics of less familiar “restricted” Dynkin diagrams.