On the theory of algebraic invariants of vector spaces of Killing tensors

We employ a hybrid version of the classical Cartan method of moving frames to develop a practical algorithm for the generation of isometry group invariants and covariants for arbitrary vector spaces of Killing tensors defined on any flat pseudo-Riemannian manifold. We then apply our algorithm to construct a set of fundamental covariants for the space of valence-two Killing tensors defined in three-dimensional Euclidean space and use them to invariantly characterize the associated eleven orthogonally separable webs.