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

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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.