论文标题
GAP-$ P $ VIRASORO代数的限制模块和某些顶点代数的扭曲模块
Restricted modules for gap-$p$ Virasoro algebra and twisted modules for certain vertex algebras
论文作者
论文摘要
本文研究了Gap-$ p $ virasoro代数$ $的限制模块及其与某些顶点代数的扭曲模块的内在连接。我们首先在限制的$ $ $ \ el $的限制$ $ - 模型与顶点algebra $ v _ {\ Mathcal {n} _ {p}} _ {p}}}（\ el，0）$的扭曲模块类别之间建立等价性。 $ \ el：=（\ ell_ {0}，0，\ cdots，0）\ in \ c^{\ half halfp+1} $， $ \ ell_ {0} \ in \ c $是Virasoro中心的动作。然后，我们将重点放在简单限制的$ $ $ $ \ el $的构建和分类上。更明确地，我们为诱导的模块提供了简单限制的$ $模型的统一结构。我们介绍了几种相同的限制$ $ $模型的特征，作为本地nilpotent（等效地，本地有限）的模块，相对于$ $ $的某些正部分。此外，简单限制的$ $ $ $ $ \ el $的模型被分类。它们是最高的重量模块或简单感应的模块。最后，我们展示了几个具体的示例，这些示例的简单限制$ $ $ $ $ \ el $（包括惠特克模块）。
This paper studies restricted modules of gap-$p$ Virasoro algebra $Ł$ and their intrinsic connection to twisted modules of certain vertex algebras. We first establish an equivalence between the category of restricted $Ł$-modules of level $\el$ and the category of twisted modules of vertex algebra $V_{\mathcal{N}_{p}}(\el,0)$, where $\mathcal{N}_{p}$ is a new Lie algebra, $\el:=(\ell_{0},0,\cdots,0)\in\C^{\halfp+1}$, $\ell_{0}\in\C$ is the action of the Virasoro center. Then we focus on the construction and classification of simple restricted $Ł$-modules of level $\el$. More explicitly, we give a uniform construction of simple restricted $Ł$-modules as induced modules. We present several equivalent characterizations of simple restricted $Ł$-modules, as locally nilpotent (equivalently, locally finite) modules with respect to certain positive part of $Ł$. Moreover, simple restricted $Ł$-modules of level $\el$ are classified. They are either highest weight modules or simple induced modules. At the end, we exhibit several concrete examples of simple restricted $Ł$-modules of level $\el$ (including Whittaker modules).
