Irreducible Representations of Finite Lie Conformal Algebras of Planar Galilean Type

Abstract

It is well known that Galilean conformal algebras play important roles in the nonrelativistic anti-de Sitter/conformal field theory correspondence. The finite Lie conformal algebras P G ( a , b ) of planar Galilean type can be viewed as Lie conformal analogues of certain planar Galilean conformal algebras. In this paper, we classify finite irreducible conformal modules over P G ( a , b ) for all complex numbers a and b.