Jon,
If you halve the torque and the rpm then the power is 1/4 of the full speed output.
The VFD system has to lower the applied voltage to the windings to keep the stator and rotor currents below a safe maximum. The main thing opposing the ac is the reactance (X) of the inductive winding on the stator. The stator resistance is normally quite low but the reactance is linear with frequency. X = 2Pi x F x L where F is the frequency in Hertz and L is the inductance in Henry's. As the frequency drops the current would go up as X is reduced, so the applied voltage is reduced to compensate. Torque to a first order is determined by the current flowing in the windings, as it generates the magnetic flux. At high frequency the reactance is now high and so to get sufficient current flowing the applied voltage has to be increased.
The rotor essentially is a massive shorted turn which when the magnetic field is applied by the stator has a very high current flowing in it. It behaves like a normal transformer where the stator is the primary winding and the rotor is the secondary winding. The rotor effectively only has 1-turn and rotor current is essentially the turns ratio between the primary and secondary, just like a static transformer. So if the stator (primary winding) has, say 100-turns then the secondary current in the rotor will be 100-times the stator current in simplified terms. Because of this the rotor current can become high enough to cause overheating.
The rotor induced magnetic flux works with the rotating flux supplied by the stator windings to produce the torque, but only when "slip" occurs, which is always the case with ac motors. If the rotor did manage to get up enough speed to equal the applied frequency then slip drops to zero and so does the torque, hence it slows down until enough slip occurs to produce the torque required to drive the load.
Below a certain rpm the cooling effect is decreased and the rotor begins to overheat. NEMA recommends that a motor should not be operated below 1/3rd of its normal speed to ensure sufficient cooling is available from the internal fan. For applications where very slow speeds are required then an external fan provided by another motor is required.