论文标题
关于Whittaker类型模块的不可约性：扭曲的模块和非亚伯Orbifolds
On irreducibility of modules of Whittaker type: twisted modules and nonabelian orbifolds
论文作者
论文摘要
在Arxiv：1811.04649中，我们扩展了关于循环Orbifold顶点代数的模块不可约可减至的Dong-Mason定理到整个类别的弱模块，并将此结果应用于Whittaker模块。在本文中，我们对这些结果进行了进一步的概括。令$ v $为具有可数维度的顶点超级巨头，让$ g $为$ \ mathrm {aut}（v）$的有限子组。假设$ h \在z（g）$中，其中$ z（g）$是组$ g $的中心。对于任何不可约的$ h $ twisted（弱）$ v $ -module $ m $，我们证明，如果$ m \ not \ cong g \ g \ g \ circ m $ for g $ in G $ in G $ in G $，则$ m $也不可用为$ v^g $ -module。我们还将此结果应用于示例，并为Neveu-Schwarz顶点超级algebras，Heisenberg Vertex代数，Virasoro Vertex操作员代数和Heisenberg-Virasoro Vertex Algebra提供了惠特克类型模块的不可约性。
In arXiv:1811.04649, we extended the Dong-Mason theorem on irreducibility of modules for cyclic orbifold vertex algebras to the entire category weak modules and applied this result to Whittaker modules. In this paper we present further generalizations of these results for nonabelian orbifolds of vertex operator superalgebras. Let $V$ be a vertex superalgebra with a countable dimension and let $G$ be a finite subgroup of $\mathrm{Aut}(V)$. Assume that $h\in Z(G)$ where $Z(G)$ is the center of the group $G$. For any irreducible $h$-twisted (weak) $V$-module $M$, we prove that if $M\not\cong g\circ M$ for all $g\in G$ then $M$ is also irreducible as $V^G$-module. We also apply this result to examples and give irreducibility of modules of Whittaker type for orbifolds of Neveu-Schwarz vertex superalgebras, Heisenberg vertex algebras, Virasoro vertex operator algebra and Heisenberg-Virasoro vertex algebra.
