  A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces
over quaternion slices with the aid of coherent states. It is proved that the
so obtained set forms a measurable field of Hilbert spaces and their direct
integral appears again as a reproducing kernel Hilbert space for a bigger
Hilbert space over the whole quaternions. Hilbert spaces over quaternion slices
are identified as representation spaces for a set of irreducible unitary group
representations and their direct integral is shown to be a reducible
representation for the Hilbert space over the whole quaternion field.
