Branching Rules and Tensor Product Decompositions in Algebraic Lie Theory

代数李理论中的分支规则和张量积分解

• 批准号: 9801442
• 负责人: Jonathan Brundan
• 金额: $ 6.65万
• 依托单位: University of Oregon Eugene
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-06-15 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801442&HistoricalAwards=false
• 关键词: Branching; Rules; Tensor; Product; Decompositions

9801442 Brundan This award supports research on the study and computation of various branching rules for modular representations of general linear groups and symmetric groups. In particular, the principal investigator is interested in determining to what extent such classical branching coefficients are equal to the analogous coefficients in the quantum versions of these problems. He hopes both to extend existing techniques based on lowering operators, and to exploit newly understood connections between branching rules and decompositions of tensor products. A parallel project is to generalize existing results on completely splittable representations for general linear groups to orthogonal and symplectic groups. The research supported concerns the representation theory of various algebraic objects including general linear groups and symmetric groups. Representation theory is an important method for determining the structure of these objects. This work has implications for a number of areas of mathematics including ring theory, group theory, topology and the study of Lie algebras.

小行星9801442 该奖项支持对一般线性群和对称群的模块化表示的各种分支规则的研究和计算。 特别是，主要研究人员感兴趣的是确定在何种程度上这样的经典分支系数等于类似的系数在量子版本的这些问题。 他希望既能扩展现有的基于降低算子的技术，又能利用分支规则和张量积分解之间新理解的联系。 一个平行的项目是推广现有的结果完全可裂表示一般线性群正交和辛群。 该研究支持各种代数对象的表示理论，包括一般线性群和对称群。 表示论是确定这些对象结构的重要方法。 这项工作的影响，一些领域的数学，包括环理论，群论，拓扑和研究李代数。