Differential-geometric criterion for kinematic integrability of equations with operators from $su(1,1)$ and $su(2)$

A necessary and sufficient condition for kinematic integrability of equations with operators belonging to the Lie algebras $su(1,1)$ and $su(2)$ is proved. The suggested criterion is related to differential-geometric consideration of the corresponding classes of kinematically integrable equations and is based on the $G$-representation of partial differential equations.