Irreducible Representations of the Five-Dimensional Rotation Group. I

Explicit matrix elements are found for the generators of the group R(5) in an arbitrary irreducible representation using the ``natural basis'' in which the representation of R(5) is fully reduced with respect to the subgroup R(4)=SU(2)⊗SU(2). The technique used is based on the well-known Racah algebra. The dimension formula is derived and the invariants are found. A family of identities is established which relates various polynomials of degree four in the generators and which holds in any representation of the group.