Matrix elements between vector hyperspherical states

Three-body symmetrized vector hyperspherical harmonic functions, realizing irreducible representations of the permutation group of three particles, are constructed and expressed in terms of Wigner D functions. Matrix elements of arbitrary two-body potentials between these hyperspherical states, including their velocity-dependent parts, are calculated analytically and expressed through the sum of products of the Wigner 3-j symbols and explicitly written functions of the radial variable.