  Representations of the rotation group may be formulated in second-quantised
language via Schwinger's transcription of angular momentum states onto states
of an effective two-dimensional oscillator. In the case of the molecular
asymmetric rigid rotor, by projecting onto the state space of rigid body
rotations, the standard Ray Hamiltonian $H(1,\kappa,-1)$ (with asymmetry
parameter $1 \ge \kappa \ge -1$), becomes a quadratic polynomial in the
generators of the associated dynamical $su(1,1)$ algebra. We point out that
$H(1,\kappa,-1)$ is in fact quadratic in the Gaudin operators arising from the
quasiclassical limit of an associated $su_q(1,1)$ Yang-Baxter algebra. The
general asymmetric rigid rotor Hamiltonian is thus an exactly solvable model.
This fact has important implications for the structure of the spectrum, as well
as for the eigenstates and correlation functions of the model.
