In this paper myriad covariant
representations of a class of C∗-algebras and automorphism groups are constructed.
The Hilbert spaces on which the representations are realized have an unusual
structure: they are direct integrals of measurable families H(⋅) of Hilbert spaces over
the spectrum of an abelian subalgebra of the C∗-algebra; the fibre spaces H(ζ) are
(in general) different separable subspaces of inseparable infinite tensor product
spaces. The representors of the algebra and the unitary representors of the group do
not decompose but act both in the fibres and on the underlying spectrum. Cases
covered by this construction include the quasifree automorphisms of the Clifford
algebra which leave a given basis fixed and the automorphism corresponding to
charge conjugation.
