Representation of classical and quantum groups

经典群和量子群的表示

• 批准号: 261452-2008
• 负责人: Stokke, Anna
• 金额: $ 0.87万
• 依托单位: University of Winnipeg
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=395030
• 关键词: Representation; classical; quantum; groups

Symmetries occur naturally in the world and are of interest to many scientists including mathematicians, chemists, and physicists. By placing an algebraic structure on the set of symmetries of an object, one obtains a group. A representation is a way of identifying a particular group with another group that has properties which allow one to extract information about the original group. Many representations are intrinsically complicated and it is desirable to find simplified methods for studying them. This proposal is concerned with the study of representations for particular groups using other mathematical objects such as Schur algebras that allow one to discover information about the original representation.

对称性在世界上自然存在，许多科学家包括数学家，化学家和物理学家都对对称性感兴趣。 通过在一个对象的对称集合上放置一个代数结构，我们得到一个群。 表示是一种将特定组与另一组进行标识的方法，该另一组具有允许提取有关原始组的信息的属性。 许多表征本质上是复杂的，因此需要找到研究它们的简化方法。 这个建议关注的是使用其他数学对象（如舒尔代数）来研究特定群的表示，这些数学对象允许人们发现有关原始表示的信息。