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

科温教授将继续他的研究， 真实的幂零李群的分析与表示理论 和约化p-adic群 在前一个领域，他将继续 和F一起工作。齐性幂零李空间上的Greenleaf 小组，特别是对问题的特点代数 这类空间的不变微分算子。 关于p- 进群，他将扩展他的工作，超尖点 表示。 这一问题在下列问题中处于中心地位： 这些群体的代表性理论。 科温教授的项目涉及到 群的表示理论 群论基本上是 研究对称性。 如果一个系统从每一点看都是一样的， 空间，则对称群包含平移群。 在特定的情况下，抽象群的知识不是 足够了，人们需要考虑集团的具体实现 换句话说，就是一种表现形式。

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.