The representation of the two-dimensional harmonic oscillator by the unitary group SU (2) simple Coriolis-adapted vibrational basis states for the treatment of vibration–rotation interaction in polyatomic molecules. The vibrational part of the zeroth-order vibration–rotation Hamiltonian is expressed in terms of the generators (Sx,Sy,Sz) of the group SU(2), leading to a coupled angular momentum representation of the vibration–rotation Hamiltonian. In the prolate limit, this leads to an effective k-dependent zeroth-order vibrational Hamiltonian that is linear in the group generators. The problem can be solved exactly in this limit by a simple axis transformation in the vibrational ‘‘spin’’ space. Because of the underlying SU(2) structure, the transformation matrix elements and overlaps of basis states of different effective Hamiltonians corresponding to different values of k are given by simple expressions involving Wigner d matrices.