Let $G$ be a simple complex Lie group with Lie algebra $\mf g$ and let $\af$be the affine Lie algebra. We use intertwining operators andKnizhnik-Zamolodchikov equations to construct a family of $\N$-graded vertexoperator algebras associated to $\mf g$. They are $\af \oplus \af$-modules ofdual levels $k, \bar k \notin \Q$ in the sense that $k + \bar k = -2 h^\vee$where $h^\vee$ is the dual Coxeter number of $\mf g$. Its conformal weight 0component is the algebra of regular functions on $G$. This family of vertexoperator algebras were previously studied by Arkhipov-Gaitsgory andGorbounov-Malikov-Schechtman from different points of view. We show that thevertex envelope of the vertex algebroid associated to $G$ and level $k$ isisomorphic to the vertex operator algebra we constructed above when $k$ isirrational. The case of integral central charges is also discussed.
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机译：假设$ G $是一个具有李代数$ \ mf g $的简单复李群，而让$ \ af $是仿射李代数。我们使用交织的算子和Knizhnik-Zamolodchikov方程构造与$ \ mf g $相关的$ \ N $级的顶点算子代数族。在$ k + \ bar k = -2 h ^ \ vee $其中$ h ^ \ vee $的意义上，它们是$ \ af \ oplus \ af $双级别模块$ k，\ bar k \ notin \ Q $是$ \ mf g $的双Coxeter数。它的保形权重0分量是$ G $上正则函数的代数。顶点运算子代数家族先前曾由Arkhipov-Gaitsgory和Gorbounov-Malikov-Schechtman从不同的角度进行研究。我们表明，与$ G $相关联的顶点代数的顶点包络和级别$ k $与我们在$ k $为非理性时在上面构造的顶点算子代数同构。还讨论了积分中央收费的情况。
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