Classification of irreducible modules of the vertex algebra $V_L^{+}$ when $L$ is a nondegenerate even lattice of an arbitrary rank

Abstract

In this paper, we first classify all irreducible modules of the vertex algebra $V_L^{+}$ when $L$ is a negative definite even lattice of arbitrary rank. In particular, we show that any irreducible $V_L^{+}$-module is isomorphic to a submodule of an irreducible twisted $V_L$-module. We then extend this result to a vertex algebra $V_L^{+}$ when $L$ is a nondegenerate even lattice of finite rank.

To appear in J. of Algebra