Classification of irreducible modules of certain subalgebras of free boson vertex algebra

Let M(1) be the vertex algebra for a single free boson. We classify irreducible modules of certain vertex subalgebras of M(1) generated by two generators. These subalgebras correspond to the -algebras with central charge 1−6(p−1)2/p where p is a positive integer, p 2. We also determine associated Zhuʹs algebras.