Refining twisted bimodules associated to VOAs

Abstract

Let $V$ be a vertex operator algebra and $g$ an automorphism of $V$ of finite order $T$. For any $m,n\in (1/T)\mathbb{N}$, an $A_{g,n}(V)-A_{g,m}(V)$ bimodule $A_{g,n,m}(V)=V/O_{g,n,m}(V)$ was defined by Dong and Jiang, where $O_{g,n,m}(V)$ is the sum of three certain subspaces $O_{g,n,m}^{\prime }(V),O_{g,n,m}^{\prime \prime }(V)$ and $O_{g,n,m}^{\prime \prime \prime }(V)$. In this paper, we show that $O_{g,n,m}(V)=O_{g,n,m}^{\prime }(V)$.