Mathematical Sciences: Representation Theory and Combinatorics

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9622985 Ram This award supports the research of Professor A. Ram to work on the connections between Lie algebras, quantum groups, Coxeter groups, their representations and combinatorics. In particular he will study representations of Iwahori-Hecke algebras and the centralizers algebras of tensor representations with special emphasis on the combinatorial aspects of these topics. For example, he hopes to obtain an explicit combinatorial formula that gives the irreducible representations as well as their irreducible characters. This is research in algebra. Algebra can be thought of as the study of symmetry in the abstract. As such, it has direct applications to areas of physics and chemistry. Much of algebra also connects directly to problems in coding theory and so has a direct bearing on the very practical problem of error correcting in data transfer.