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

• Autores: Minxian Zhu
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 5, 2008, págs. 1513-1547
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.07.005
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• Resumen

  • Let G be a simply-connected complex Lie group with simple Lie algebra and let be its affine Lie algebra. We use intertwining operators and Knizhnik�Zamolodchikov equations to construct a family of -graded vertex operator algebras (VOAs) associated to . These vertex operator algebras contain the algebra of regular functions on G as the conformal weight 0 subspaces and are -modules of dual levels in the sense that , where h is the dual Coxeter number of . This family of VOAs was previously studied by Arkhipov�Gaitsgory and Gorbounov�Malikov�Schechtman from different points of view. We show that when k is irrational, the vertex envelope of the vertex algebroid associated to G and the level k is isomorphic to the vertex operator algebra we constructed above. The case of rational levels is also discussed