Mathematical Sciences: Representation Theory and Combinatorics

小行星9622985 该奖项支持了A教授的研究。拉姆工作之间的联系李代数，量子群，考克斯特群，他们的代表性和组合。特别是，他将研究表示岩堀-赫克代数和中心化代数的张量表示，特别强调组合方面的这些议题。例如，他希望得到一个明确的组合公式，给出不可约表示及其不可约字符。 这是代数研究。 代数可以被认为是抽象的对称性的研究。因此，它直接应用于物理和化学领域。许多代数也直接联系到编码理论中的问题，因此与数据传输中的纠错这一非常实际的问题有直接关系。

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.