Mathematical Sciences: Representation Theory and Differential Geometry

首席研究员将研究 SO（4，4）的最小表示的数学物理， 完全可积系统的"哈密尔顿算子对 算子，"零锥上的G不变微分算子， Lusztig的基本定理 主要研究者拟承担的项目 涉及群论的技术并会产生后果 数学物理学中。 群是一个抽象的代数 一个简单的概念，它只涉及一个数字的集合或 变量和一个规定的方式组合他们服从 某些规则。 用加法运算的整数是一个 一个群体的例子。 20世纪70年代的数学物理学家 理解亚原子粒子之间的关系 用群论来描述，群论已经研究了 多年来，代数学家。

The principal investigator will study the implications in mathematical physics of the minimal representation of SO(4,4), completely integrable systems using "pairs of Hamiltonian operators," G-invariant differential operators on the nil-cone, and Lusztig's basis theorem. The project to be undertaken by the principal investigator involves techniques from group theory and will have consequences in mathematical physics. A group is an abstract algebraic concept which simply involves a collection of numbers or variables and a prescribed manner of combining them which obeys certain rules. The integers with the operation of addition is an example of a group. By the 1970s mathematical physicists understood that relationships between subatomic particles could be described using the group theory which had been studied for many years by algebraists.