Abstract
Let M-n = SO(n) (sic) R-n, n >= 2, be the classical motion group, where SO(n) acts on Rn by rotation. In this paper, we identify the dual space (M) over cap (n), i.e. the set of equivalence classes of irreducible unitary representations of M-n, with the quotient space of admissible co-adjoint orbits m(n)(double dagger)/M-n via a nice geometric parameterization of the two spaces. We showthen that this identification is a homeomorphism.