Mathematical Sciences: Representation Theory and Combinatorics

本研究的重点是李代数、李群、量子群的表示及其组合学。主要研究内容包括：(1)张量表示的中心化子代数；(2)Weyl群对称函数；(3)分支规则和中心化子代数；(4)Kac-Moody李代数的权和根的多重性。这项研究涉及一种名为李代数的数学对象。李代数起源于另一个叫做李群的物体。李群的一个例子是球体的旋转，其中一个旋转之后是另一个旋转。李群和李代数在涉及球面运动分析的领域中很重要。

The focus of this research is on the representations of Lie algebras, Lie groups, and quantum groups, and their combinatorics. The principal investigator will work on (1) centralizer algebras of tensor representations; (2) Weyl group symmetric functions; (3) branching rules and centralizer algebras; and (4) weight and root multiplicities for Kac-Moody Lie algebras. This research is concerned with a mathematical object called a Lie algebra. Lie algebras arise from another object called a Lie group. An example of a Lie group is the rotations of a sphere where one rotation is followed by another. Lie groups and Lie algebras are important in areas involving analysis of spherical motion.