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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 W(2, 2p-1)--algebras with central charge $1- 6 (p - 1)^2 / p$ where p is a positive integer, $p \ge 2$. We also determine associated Zhu's algebras.

Vertex algebras; W algebras; irreducible representations; free boson

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