Abstract
Let be the planar Galilean conformal algebra and be its universal central extension. Then (resp. ) admits a triangular decomposition: (resp. ). In this paper, we study universal and generic Whittaker -modules (resp. -modules) of type where 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 is simple if and only if 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.
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