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.
Categories: math-ph math.MP