Vertex operator algebras associated to modified regular representations of affine Lie algebras

dc.creatorZhu, Minxian
dc.date2006-11-17
dc.date2007-11-20
dc.date.accessioned2026-07-07T08:43:50Z
dc.date.available2026-07-07T08:43:50Z
dc.descriptionLet $G$ be a simple complex Lie group with Lie algebra $\mf g$ and let $\af$ be the affine Lie algebra. We use intertwining operators and Knizhnik-Zamolodchikov equations to construct a family of $\N$-graded vertex operator algebras associated to $\mf g$. They are $\af \oplus \af$-modules of dual 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 0 component is the algebra of regular functions on $G$. This family of vertex operator algebras were previously studied by Arkhipov-Gaitsgory and Gorbounov-Malikov-Schechtman from different points of view. We show that the vertex envelope of the vertex algebroid associated to $G$ and level $k$ is isomorphic to the vertex operator algebra we constructed above when $k$ is irrational. The case of integral central charges is also discussed.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/0611517
dc.identifierhttp://arxiv.org/abs/math/0611517
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142454
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B69, 17B67
dc.titleVertex operator algebras associated to modified regular representations of affine Lie algebras
dc.typetext

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