Mathematical Sciences: Quantum Kac-Moody Groups and RelatedQuestions

小行星9623327 这项拨款支持Y教授的研究。Soibelman工作的各种问题的理论卡茨穆迪集团。特别是他将研究问题所产生的张量结构理论的量子仿射代数和复合版本的李双代数。然后，他将这些结果应用到量子τ函数和量子外尔函数。最后，他希望研究手性问题的理论量子群。 这是一项从代数领域开始的研究，但超越了代数领域，涉及数论和理论物理。 这些联系的原因是，代数可以被看作是对抽象对称性的研究。因此，代数在物理和化学领域有直接的应用。特别是现代物理学中的规范场理论广泛地使用了这一领域的代数，本项目将详细研究其中的一些联系。还有编码理论和跨通信线路的数据传输。

9623327 Soibelman This grant supports the research of Professor Y. Soibelman to work on various problems in the theory of Kac-Moody groups. In particular he will study problems arising from the tensor structures in the theory of quantum affine algebras and compound versions of Lie bialgebras. He then will apply these results to quantum tau functions and quantum Weyl functions. Finally, he wishes to study chiral problems in the theory of quantum groups. This is research that starts out in the field of algebra but moves beyond that to touch both number theory and theoretical physics. The reasons for these connections are that algebra can be though of as the study of symmetry in the abstract. As such algebra has direct applications to areas of physics and chemistry. In particular the modern theory of gauge fields in physics uses this area of algebra extensively and this project will study some of these connections at length. There are also connections to coding theory and the transmission of data across communication lines.