手征代数上的微分算子与loop群
Differential operators and the loop group via chiral algebras
摘要：
设$G$是一个代数群，$\widetilde{\mathfrak g}$是某个水平上的仿射代数.考虑导出模$V:=Ind^{\widetilde{\mathfrak g}}_{{\mathfrak g}[[t]](O_{G[[t]]})$，其中$O_{G[[t]]}$是群$G[[t]]$上的正则函数环。本文证明了$V$自然是一个顶点算子代数，它负责循环群$G((t))$上的D-模。利用VOA技巧证明了$V$实际上是仿射代数上的双模.此外，我们表明，$V$具有显着的属性，其BRST减少相对于$\widetilde{\mathfrak g}$。本文有相当大的交叉与最近预印本Gorbunov，Malikov和Schechtman。
英文摘要：
Let $G$ be an algebraic group and let $\widetilde{\mathfrak g}$ be the corresponding affine algebra on some level. Consider the induced module $V:=Ind^{\widetilde{\mathfrak g}}_{{\mathfrak g}[[t]](O_{G[[t]]})$, where $O_{G[[t]]}$ is the ring of regular functions on the group $G[[t]]$. In this paper we show that $V$ is naturally a vertex operator algebra, which is "responsible" for D-modules on the loop group $G((t))$. Using the techiques of VOA we show that $V$ is in fact a bimodule over the affine algebra. In addition, we show that $V$ possesses a remarkable property related to its BRST reduction with respect to $\widetilde{\mathfrak g}$. This paper has a considerable intersection with a recent preprint of Gorbunov, Malikov and Schechtman.
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