Whittaker modules for the planar Galilean conformal algebra and its central extension

Let G be the planar Galilean conformal algebra and (G) over tilde be its universal central extension. Then G (resp. (G) over tilde) admits a triangular decomposition: G = G(+)circle plus G(0) circle plus G(-) (resp. (G) over tilde = (G) over tilde (+) circle plus (G) over tilde (0) circle plus (G) over tilde (-)). In this paper, we study universal and generic Whittaker G-modules (resp. (G) over tilde -modules) of type phi, where phi : G(+) congruent to (G) over tilde (+) -> C is a Lie algebra homomorphism. We classify the isomorphism classes of universal and generic Whittaker modules. Moreover, we show that a generic Whittaker module of type phi is simple if and only if phi is nonsingular. For the nonsingular case, we completely determine the Whittaker vectors in universal and generic Whittaker modules. For the singular case, we concretely construct some proper submodules of generic Whittaker modules.