论文标题
仿射顶点代数的正能表示
Positive energy representations of affine vertex algebras
论文作者
论文摘要
我们使用本地化技术构建了仿射顶点代数的积极能量表示的新家族以及它们的自由场实现。我们介绍了扭曲函数T_αON的类别。这两个函子通勤和Wakimoto函子的图像由放松的Wakimoto \ wideHat {g}_κ模块组成。特别是，将扭曲函数t_α应用于轻松的wakimoto \ widehat {g}_κ模块，其顶级成分对verma g-module m^g_b（λ）是同构的，我们获得了轻松的wakimoto \ wakimoto \ wakimoto \ wideHat {g wideHat {g}_κ-模块的最高组成部分是acomort and and and and and-ins and ins and and and。 g模块w^g_b（λ，α）。我们表明，放松的维尔马模块和放松的wakimoto模块，其顶级成分是这样的α-gelfand-tsetlin模块，通常是同构的。这是Wakimoto模块的E.frenkel结果的类似物。对于G的抛物线亚代词P，我们在p诱导的广义VERMA模块的扭曲函数下，构建了一个可允许的G模型的大家族，作为图像。通过这种方式，我们获得了简单仿射顶点代数的新的简单正能表示。
We construct new families of positive energy representations of affine vertex algebras together with their free field realizations by using localization technique. We introduce the twisting functor T_αon the category of modules over affine Kac--Moody algebra \widehat{g}_κof level κfor any positive root αof g, and the Wakimoto functor from a certain category of g-modules to the category of smooth \widehat{g}_κ-modules. These two functors commute and the image of the Wakimoto functor consists of relaxed Wakimoto \widehat{g}_κ-modules. In particular, applying the twisting functor T_αto the relaxed Wakimoto \widehat{g}_κ-module whose top degree component is isomorphic to the Verma g-module M^g_b(λ), we obtain the relaxed Wakimoto \widehat{g}_κ-module whose top degree component is isomorphic to the α-Gelfand--Tsetlin g-module W^g_b(λ, α). We show that the relaxed Verma module and relaxed Wakimoto module whose top degree components are such α-Gelfand--Tsetlin modules, are isomorphic generically. This is an analogue of the result of E.Frenkel for Wakimoto modules both for critical and non-critical level. For a parabolic subalgebra p of g we construct a large family of admissible g-modules as images under the twisting functor of generalized Verma modules induced from p. In this way, we obtain new simple positive energy representations of simple affine vertex algebras.
