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

9600124 Kleshchev这笔赠款支持A.Kleschev教授研究有限群的模表示中的问题。特别地，他想找出n阶对称群的不可约表示的某些合成因子的乘性。他还想通过量子群理论以及交错群和不可约Speht模的不可约表示的研究来研究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，这个领域在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，使用群论的技术解决了许多与数据传输中的问题有关的问题。还有与纠错码的直接连接，这些纠错码对现代计算至关重要，例如与CD-ROM一起工作。

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.