论文标题
定期表示和$ a_ {n}（v）$ - $ a_ {m}（v）$ bimodules
Regular representations and $A_{n}(V)$-$A_{m}(V)$ bimodules
论文作者
论文摘要
本文是为了在顶点操作员代数$ v $和$ a_ {n}（v）$ - $ a_ {m}（m}（v）$ bimodules of dong and jiang的定期表示之间建立自然连接。让$ w $为弱$ v $ - 模块，让$（m，n）$是一对非负整数。我们研究两个商空间$ a_ {n，m}^{\ dagger}（w）$和$ a^{\ diamond} _ {n，m}（w）$ w $。 事实证明，双空间$ a^{\ dagger} _ {n，m}（w）^{*} $被视为$ w^*$的子空间与级别 - $（m，n）$（m，n）$ vacuum的定期表示模块$ \ mathfrak $ \ nathfrak {d} d} _ {d} _ {（-1）}的级别的子空间。通过使用此连接，我们获得了$ a_ {n}（v）$ - $ a_m（v）$ bimodule结构，这两个$ a_ {n，m}^{\ dagger}（w）$和$ a^{\ diamond} _ {\ diamond} _ {n，m}（w）$。此外，我们获得了$ \ n $ graded弱$ v $ - 模块结构，并在$ a^{\ diamond} _ {\ diamond} _ {\ box，m}（m}（w）上的通勤$ a_m（v）$ - 模块结构上因此，我们恢复了相应的结果，并大致确认了Dong和Jiang的猜想。
This paper is to establish a natural connection between regular representations for a vertex operator algebra $V$ and $A_{n}(V)$-$A_{m}(V)$ bimodules of Dong and Jiang. Let $W$ be a weak $V$-module and let $(m,n)$ be a pair of nonnegative integers. We study two quotient spaces $A_{n,m}^{\dagger}(W)$ and $A^{\diamond}_{n,m}(W)$ of $W$. It is proved that the dual space $A^{\dagger}_{n,m}(W)^{*}$ viewed as a subspace of $W^*$ coincides with the level-$(m,n)$ vacuum subspace of the regular representation module $\mathfrak{D}_{(-1)}(W)$. By making use of this connection, we obtain an $A_{n}(V)$-$A_m(V)$ bimodule structure on both $A_{n,m}^{\dagger}(W)$ and $A^{\diamond}_{n,m}(W)$. Furthermore, we obtain an $\N$-graded weak $V$-module structure together with a commuting right $A_m(V)$-module structure on $A^{\diamond}_{\Box,m}(W):=\oplus_{n\in \N}A^{\diamond}_{n,m}(W)$. Consequently, we recover the corresponding results and roughly confirm a conjecture of Dong and Jiang.
