Mathematical Sciences: Topics in Analysis on Real and p-adicLie Groups

Corwin和Goodman教授将进行广泛的 李群表示论研究大纲 和相关物体。科温的部分工作将涉及 齐型空间上的不变微分算子 幂零群他还将研究超尖瓣 p-adic groups的定义古德曼将继续 研究当前代数和循环的表示 组高阶Sugawara的代数性质 将使用张量不变量理论来研究算子 对于古典团体来说。几何学的分析方面 环群的正能量表示模型将是 考察古德曼还将寻求新类型的惠特克模型 对于真实的约化群的表示。 这个项目与谎言的表征理论有关 群（及其表兄弟，李代数）， 挪威数学家Sophus Lie。一个基本的例子 李群是球体的旋转群，其中群 操作包括一个动作接着另一个动作。详细 关于这个群体的信息非常有助于解决 球对称的数学或物理问题 礼物其他的运动组也有其他的对称性。 一个更代数（相对于几何）的例子来源， 李群来自矩阵的乘法。本集团 对于给定大小的所有可逆真实的（或复）矩阵， 李群，就像它的任何子群一样， 以自然的方式描述。能去是令人向往的 在几何点和代数点之间来回 例如，考虑到许多方法， 球体的旋转组可以被实现为一组 可逆矩阵这就是表象理论。 关于给定群体的表示的事实倾向于存储一个 大量的信息非常经济。取决于 这一信息可能会影响到 从数论到数学物理的几乎所有学科。 科温教授和古德曼教授的项目跨越了一个博览会， 部分应用和当代的重点 表示理论

Professors Corwin and Goodman will pursue a wide-ranging program of research in the representation theory of Lie groups and related objects. Part of Corwin's work will deal with invariant differential operators on homogeneous spaces of nilpotent groups. He will also study supercuspidal representations of p-adic groups. Goodman will continue investigating the representations of current algebras and loop groups. The algebraic properties of higher-order Sugawara operators will be studied using the theory of tensor invariants for the classical groups. Analytic aspects of the geometric models for positive-energy representations of loop groups will be examined. Goodman will also seek new types of Whittaker models for representations of real reductive groups. This project has to do with the representation theory of Lie groups (and of their cousins, Lie algebras), which bear the name of the Norwegian mathematician Sophus Lie. One basic example of a Lie group is the group of rotations of a sphere, where the group operation consists of following one motion by another. Detailed information concerning this group is very helpful in solving mathematical or physical problems in which spherical symmetry is present. Other groups of motions capture other kinds of symmetry. A more algebraic (as opposed to geometric) source of examples of Lie groups comes from the multiplication of matrices. The group of all invertible real (or complex) matrices of a given size is a Lie group, as is just about any subgroup thereof that can be described in a natural manner. It is desirable to be able to go back and forth between the geometric and algebraic points of view, for instance to consider the numerous ways in which the rotation group of the sphere can be realized as a group of invertible matrices. This, roughly, is representation theory. Facts about the representations of a given group tend to store a lot of information very economically. Depending on where the group in question comes from, this information can impinge on almost any subject from number theory to mathematical physics. The project of Professors Corwin and Goodman spans a fair portion of the applications and emphases of contemporary representation theory