Representation Theory of the Virasoro Algebra
Representation Theory of the Virasoro Algebra
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DOI：
10.1007/978-0-85729-160-8
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发表时间：
2010-11
期刊：
影响因子：
--
通讯作者：
K. Iohara;Y. Koga
中科院分区：
文献类型：
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作者：
K. Iohara;Y. Koga
Virasoro代数是一个无限维李代数，在数学和理论物理中起着越来越重要的作用。这本书描述了一些基本事实的代表性理论的Virasoro代数在一个独立的方式。主题包括Verma模块和Fock模块的结构，（unitarizable）Harish-Chandra模块的分类，倾斜等价，以及与所谓的最小级数表示相关的有理顶点算子代数。涵盖了广泛的材料，这本书有三个附录，其中提供了一些章节所需的背景资料。作者以统一的方式组织基本结果，并改进现有的证明。例如，在第三章中，我们用代数的方法重新表述了Jantzen滤波的推广，并给出了几何解释。对被广泛认为是正确的陈述进行了整理，并证明了已知但未被验证的结果，如第八章中Fock模的修正结构定理。这本书将感兴趣的范围广泛的数学家和物理学家从研究生到研究人员的水平。
The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of the Virasoro algebra in a self-contained manner. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and the rational vertex operator algebras associated to the so-called minimal series representations. Covering a wide range of material, this book has three appendices which provide background information required for some of the chapters. The authors organize fundamental results in a unified way and refine existing proofs. For instance in chapter three, a generalization of Jantzen filtration is reformulated in an algebraic manner, and geometric interpretation is provided. Statements, widely believed to be true, are collated, and results which are known but not verified are proven, such as the corrected structure theorem of Fock modules in chapter eight. This book will be of interest to a wide range of mathematicians and physicists from the level of graduate students to researchers.