Mathematical Sciences: Branching Rules for Symmetric Groups and Hecke Algebras via Algebraic and Quantum Groups

数学科学：通过代数和量子群的对称群和赫克代数的分支规则

• 批准号: 9600124
• 负责人: Alexander Kleshchev
• 金额: $ 6.69万
• 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: 1996
• 资助国家: 美国
• 起止时间: 1996-06-15 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9600124&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Branching; Rules; Symmetric

9600124 Kleshchev This grant supports the research of Professor A. Kleschev to work on problems in the modular representation of the finite groups. In particular he wants to find the mutiplicities of some composition factors of an irreducible representation of the symmetric group of order n. He also want to study branching rules for Hecke algebras via the theory of quantum groups and the study of irreducible representations of the alternating group and irreducible Specht modules. This is research in the field of group theory. Group theory can be thought of as the study of symmetry in the abstract. As such, this area has direct applications to many areas of physics and chemistry. Moreover, within the last 30 years, many connections to problems in data transmission have been solved using techniques from group theory. There are also direct connections to the error correcting codes that are vital for modern computing such as working with CD-ROM's.

9600124 Kleschev这笔经费用于支持A. Kleschev教授研究有限群的模表示问题。他特别想找到n阶对称群的不可约表示的一些组成因子的多重性。他还想通过量子群理论和交替群的不可约表示和不可约的Specht模的研究来研究Hecke代数的分支规则。这是群论领域的研究。群论可以被认为是对抽象对称性的研究。因此，这个领域对物理和化学的许多领域都有直接的应用。此外，在过去的30年里，许多与数据传输问题有关的问题已经用群论的技术解决了。还有与纠错码的直接联系，纠错码对现代计算至关重要，比如使用CD-ROM。