The concomitants of a prehomogeneous vector space

The classical method of radial separation of variables is applied to gain some information about the concomitants, also known as relatively equivariant polynomial maps or covariants, of a class of prehomogeneous vector spaces. Particular attention is payed to concomitants that are themselves prehomogeneous. The results are applied to classify all prehomogeneous concomitants of several examples of interest in arithmetic.