论文标题
顶点操作员代数的扭曲定期表示
Twisted regular representations of vertex operator algebras
论文作者
论文摘要
本文是研究我们称之为顶点操作员代数的扭曲的常规表示形式。令$ v $为顶点操作员代数，令$σ_1，σ_2$为$ v $的有限顺序自动形态，让$σ=（σ_1σ_2）^{ - 1} $。在主要结果中，对于任何$σ$ -Twisted $ v $ -module $ w $和任何非零复合$ z $，我们构造一个弱$σ_1\ outimesσ_2$ -Twisted $ v \ otimes v $ v $ -module $ \ mathfrak $ \ mathfrak $ \ mathfrak {d} $ $ W^{*} $。令$ w_1，w_2 $为$σ_1$ -Twisted，$σ_2$ -Twisted $ v $ -modules。 We show that $P(z)$-intertwining maps from $W_1\otimes W_2$ to $W^{*}$ are the same as homomorphisms of weak $σ_1\otimes σ_2$-twisted $V\otimes V$-modules from $W_1\otimes W_2$ into $ \ mathfrak {d} _ {σ_1，σ_2}^{（z）}（w）$。我们还表明，从$ w_1 \ otimes w_2 $到$ w^{*} $交织的$ p（z）$ - 相互交织。 w_2} $，这是黄和莱波斯基结果的扭曲版本。最后，我们表明，对于每种$τ$ -Twist的$ V $ -MODULE $ M $，$τ$带有$ V $的任何有限级自动形态，$ q $ raded trace函数的系数在$ \ mathfrak {d} _ {d} _ {_ {τ，τ^，τ^{-1}}}^$ nime $τ\ otimesτ^{ - 1} $ - 扭曲的$ v \ otimes v $ -subModule同构为$ m \ otimes m'$。
This paper is to study what we call twisted regular representations for vertex operator algebras. Let $V$ be a vertex operator algebra, let $σ_1,σ_2$ be commuting finite-order automorphisms of $V$ and let $σ=(σ_1σ_2)^{-1}$. Among the main results, for any $σ$-twisted $V$-module $W$ and any nonzero complex number $z$, we construct a weak $σ_1\otimes σ_2$-twisted $V\otimes V$-module $\mathfrak{D}_{σ_1,σ_2}^{(z)}(W)$ inside $W^{*}$. Let $W_1,W_2$ be $σ_1$-twisted, $σ_2$-twisted $V$-modules, respectively. We show that $P(z)$-intertwining maps from $W_1\otimes W_2$ to $W^{*}$ are the same as homomorphisms of weak $σ_1\otimes σ_2$-twisted $V\otimes V$-modules from $W_1\otimes W_2$ into $\mathfrak{D}_{σ_1,σ_2}^{(z)}(W)$. We also show that a $P(z)$-intertwining map from $W_1\otimes W_2$ to $W^{*}$ is equivalent to an intertwining operator of type $\binom{W'}{W_1\; W_2}$, which is a twisted version of a result of Huang and Lepowsky. Finally, we show that for each $τ$-twisted $V$-module $M$ with $τ$ any finite-order automorphism of $V$, the coefficients of the $q$-graded trace function lie in $\mathfrak{D}_{τ,τ^{-1}}^{(-1)}(V)$, which generate a $τ\otimes τ^{-1}$-twisted $V\otimes V$-submodule isomorphic to $M\otimes M'$.
