  l-Conformal Galilei algebra, denoted by g{l}{d}, is a non-semisimple Lie
algebra specified by a pair of parameters (d,l). The algebra is regarded as a
nonrelativistic analogue of the conformal algebra. We derive hierarchies of
partial differential equations which have invariance of the group generated by
g{l}{d} with central extension as kinematical symmetry. This is done by
developing a representation theory such as Verma modules, singular vectors of
g{l}{d} and vector field representations for d = 1, 2.
