Mathematical Sciences: Topics in Analysis on Real and P-Adic Lie Groups

Corwin教授将继续研究实幂零李群和约p进群的调和分析和表示理论。在前一个领域，他将继续与F. Greenleaf一起研究幂零李群的齐次空间，特别是刻画这种空间的不变微分算子的代数问题。关于p进群，他将扩展他在超尖表示方面的工作。这个问题是这些群体的代表性理论的核心问题。考文教授的课题涉及群体表征理论中的问题。群论基本上是对对称性的研究。如果一个系统从空间的每一点看都是一样的，那么对称群就包含平移群。在特殊情况下，对抽象群的了解是不够的，需要考虑转换群的具体实现，换句话说，是一种表示。

Professor Corwin will continue his investigations in harmonic analysis and representation theory for real nilpotent Lie groups and reductive p-adic groups. In the former area he will continue work with F. Greenleaf on homogeneous spaces of nilpotent Lie groups, particularly on problems characterizing the algebra of invariant differential operators for such spaces. Concerning p- adic groups, he will extend his work on supercuspidal representations. This problem is central in questions of representation theory for these groups. Professor Corwin's project involves questions in the representation theory of groups. Group theory is basically the study of symmetry. If a system looks the same from every point in space then the symmetry group contains the group of translations. In particular situations, a knowledge of the abstract group is not enough and one needs to consider concrete realizations of the group of transformations, in other words, a representation.