Irreducible Modules Over the Universal Central Extension of the Planar Galilean Conformal Algebra

ABSTRACT In this paper, we study the representation theory of the universal central extension of the infinite‐dimensional Galilean conformal algebra, introduced by Bagchi–Gopakumar, in dimensional space‐time, which was named the planar Galilean conformal algebra by Aizawa. More precisely, we construct a family of Whittaker modules over while the necessary and sufficient conditions for these modules to be irreducible are given when , and have the same parity. Moreover, the irreducible criteria of the tensor product modules over are obtained, where are ‐free modules of rank one over and is an irreducible restricted module over . Also, the isomorphism classes of these tensor product modules are determined.