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Representation theory of an infinite dimensional Galilean conformal algebraintroduced by Martelli and Tachikawa is developed. We focus on the algebradefined in (2+1) dimensional spacetime and consider central extension. It isthen shown that the Verma modules are irreducible for non-vanishing highestweights. This is done by explicit computation of Kac determinant. We alsopresent coadjoint representations of the Galilean conformal algebra and its Liegroup. As an application of them, a coadjoint orbit of the Galilean conformalgroup is given in a simple case.

Some representations of planar Galilean conformal algebra