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

Abstract

In this paper, we study universal and generic Whittaker G-modules (resp. G-modules) of type φ, where φ : G + = G + −→ C is a Lie algebra homomorphism. We classify the isomorphism classes of universal and generic Whittaker modules. Moreover, we show that a generic Whittaker modules of type φ is irreducible if and only if φ 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.