Mathematical Sciences: Representation Theory: Quantum Groupsand Algebraic Groups

数学科学：表示论：量子群和代数群

• 批准号: 9216310
• 负责人: Zongzhu Lin
• 金额: $ 3.55万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9216310&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representation; Theory; Quantum

This research is concerned with the representation theory of quantum groups and its relation with the modular representation theory of an algebraic group. The principal investigator will study the compatibility of the Jantzen filtrations for Weyl modules and quantum Weyl modules; the structure of Weyl modules with highest weights in the non-generic position; and the structure of cohomology modules related to induction functors for both the algebraic group and the quantum groups, and the relations between them. A group is an algebraic structure with an operation defined on it. A group is called an algebraic group if its elements satisfy a polynomial identity. Algebraic groups are important for several different areas of mathematics, as well as physics.

本研究涉及的是 量子群及其与模表示的关系 代数群的理论 主要研究者将 研究了外尔氏Jantzen过滤法的相容性 模与量子Weyl模; Weyl模的结构 在非通用位置中具有最高权重;并且 与诱导函子有关的上同调模的结构 代数群和量子群， 他们之间的关系。 群是一种代数结构，定义了一种运算 一个群叫做代数群，如果它的元素 满足多项式恒等式。 代数群很重要 数学和物理的几个不同领域。