Representations of Infinite-Dimensional Lie Algebras and Quantum Groups

9970493申请者将研究量子仿射代数、无限维李代数和麦克唐纳多项式的表示理论问题。他将继续研究对称函数的顶点算子方法。特别是，他将利用这一点来研究仿射正则基在麦克唐纳多项式方面的实现，并将研究其在晶体碱中的应用。此外，他将使用最新的量子楔形模块方法来研究完美的晶体基。本课题研究量子仿射代数和顶点算子代数，它们是李代数和李群的最新推广。李代数和量子群的研究旨在揭示自然界中存在的更多对称性。这种对称性对于本世纪最重要的科学理论之一——量子力学和量子场论至关重要。

9970493The proposer will work on problems in representation theory of quantumaffine algebras, infinite-dimensional Lie algebras and Macdonald polynomials. He will continue to develop the vertex operator approach to symmetric functions. In particular he will use this to study the realization of affine canonical basis in terms of Macdonald polynomials and will also investigate its application to crystal bases. In addition he will use the recent method of quantum wedge modules to study perfect crystal bases.This project studies quantum affine algebras and vertex operator algebras, which are recent generalizations of Lie algebras and Lie groups. The study of Lie algebras and quantum groups is aimed at revealing more symmetry that existed in nature. This symmetry is crucial to the theory of quantum mechanics and quantum field theory, one of the most important scientific theories in this century.