Wandering Vectors and Frame Representations in Quaternionic Hilbert Spaces

We develop the theory of wandering vectors and frame representations in separable right quaternionic Hilbert spaces. We introduce the local commutant and obtain operator-theoretic characterizations of complete wandering vectors and normalized tight frame vectors. We prove that every complete normalized tight frame vector admits a dilation to a complete wandering vector in a larger quaternionic Hilbert space. Finally, we show that every quaternionic frame representation of a discrete group is unitarily equivalent to a subrepresentation of the left regular representation, yielding a canonical model for such representations.