The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order $2$

Abstract

Let $V_L$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_L$ induced from the $-1$ symmetry of $L$, and $V_L^{+}$ the fixed point subalgebra of $V_L$ under the action of $\theta$. We classify the irreducible weak $V_L^{+}$-modules and show that any irreducible weak $V_L^{+}$-module is isomorphic to a weak submodule of some irreducible weak $V_L$-module or to a submodule of some irreducible $\theta$-twisted $V_L$-module.

182 pages; Corrected typos

References in corpus (2)

• C_2-cofiniteness of cyclic-orbifold models
• Simple weak modules for the fixed point subalgebra of the Heisenberg vertex operator algebra of rank $1$ by an automorphism of order $2$ and Whittaker vectors