Representations of the Planar Galilean Conformal Algebra

In this paper, the planar Galilean conformal algebra G is investigated, which is an infinite-dimensional extension of the finite-dimensional Galilean conformal algebra in ( 2 + 1 ) dimensional space-time. We study simple restricted modules over G , including the highest weight modules and Whittaker modules. More precisely, we use simple modules over the finite-dimensional solvable Lie algebras to construct many simple restricted modules over G . Also, we present several equivalent descriptions for simple restricted modules over G .