Mathematical Sciences: Representations of Affine Lie Algebras and Quantum Groups and Conformal Field Theory

9401215马利科夫该奖项支持仿射李代数和量子群的表示理论的研究。主要研究人员将致力于(1)在旗形上用多值函数实现的仿射李代数模；(2)临界水平上的Wess-Zumino-Witten模型；(3)代数和几何中的复幂；(4)量子群的Gel‘fand-Kirillov猜想。许多不同的代数对象可以表示为其他代数对象的代数变换集。通过这些表示法可以确定它们的结构。本课题主要研究无限维李代数的表示理论。对这些代数的研究在整个数学和数学物理中都有应用。***

9401215 Malikov This award supports research on the representation theory of affine Lie algebras and quantum groups. The principal investigator will work on (1) affine Lie algebra modules realized in multi-valued functions on a flag manifold; (2) Wess-Zumino-Witten model at a critical level; (3) complex powers in algebra and geometry; and (4) the Gel'fand-Kirillov conjecture for quantum groups. Many different algebraic objects can be represented as algebraic sets of transformations of other algebraic objects. Through these representations their structure can be determined. This project is concerned with the representation theory of infinite dimensional Lie algebras. The study of these algebras has applications throughout mathematics and mathematical physics. ***