On Relative Invariants
A general theorem governing the precise number of relative invariants for general multiplier representations of Lie group actions is proved. A wide variety of applications, including the existence of invariant vector fields, invariant differential forms, invariant differential operators, differential invariants, and invariant connections and metrics, are discussed.
On relative invariants, M.E. Fels, P.J. Olver, Mathematische Annalen, 308(4), 1997, 701-732.