Mathematical Sciences: Geometric Aspects of Representations of Quantum Groups and Kac-Moody Lie Algebras

数学科学：量子群和 Kac-Moody 李代数表示的几何方面

• 批准号: 9202280
• 负责人: Vadim Schechtman
• 金额: $ 9.15万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9202280&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Aspects; Representations

This research is concerned with the study of representations and cohomology of Kac-Moody Lie algebras and quantum groups and their relationship with the geometry of configuration spaces and infinite flag varieties, and some related questions. The principal investigator will study the connection between representations of quantum groups and perverse sheaves in configuration spaces; cohomology of affine Lie algebras and cohomology of configuration spaces; vertex operators and cohomology of affine lie algebras; connections with the geometry of infinite flag spaces; Selberg integrals, the structure constants of operator algebras in conformal field theory, and their analogues over finite fields; and higher dimensional generalizations. Quantum groups are a new area of research for both mathematicians and physicists. On the mathematical side, it combines three of the oldest areas of "pure" mathematics, algebra, analysis and geometry, yet it is of great interest to physicists working on conformal quantum field theory.

这项研究涉及Kac-Moody Lie代数和量子组的表示和共同体的研究及其与配置空间和无限标志品种的几何形状的关系，以及一些相关的问题。 主要研究者将研究量子组的表示与构型空间中不良或骨之间的联系。仿射代数和配置空间的共同学的共同体； Aggine Like代数的顶点操作员和共同体；与无限旗空间的几何形状的连接； Selberg积分，在保形场理论中的操作器代数的结构常数及其对有限领域的类似物；和更高的维度概括。 量子组是数学家和物理学家的新研究领域。 在数学方面，它结合了“纯”数学，代数，分析和几何学的三个最古老的领域，但对于从事保形量子量理论的物理学家来说，它引起了极大的兴趣。