Fraction representations and highest-weight-like representations of the Virasoro algebra

In this paper two new classes of irreducible modules over the centerless Virasoro algebra V are obtained. These modules are generally not weight modules or Whittaker modules. We first construct a class of modules over V parameterized by any 2n+2 complex numbers for any nonnegative integer n which we call fraction modules. The necessary and sufficient conditions for fraction modules to be irreducible are determined. Also we determine the necessary and sufficient conditions for two irreducible fraction modules to be isomorphic. Then we define highest-weight-like Verma modules over V. These modules behave like highest weight Verma modules. It is proved that each highest-weight-like Verma module has an irreducible quotient module which is isomorphic to a subquotient of some reducible fraction module.