Mathematical Sciences: Lie Groups

沃尔夫教授将继续他对李群的研究， 调和分析和表示理论，与一些 复分析、黎曼几何和控制的应用 理论 他将把他最近的成果应用于 各种构造表示方法的等价性。 他将研究确定一个人性格的可能性。 从他用R导出的公式中得到的表示。赫伯，他会的 完成了关于一般半单李的Schwartz空间的工作 组和研究离散系列表示的群体 埃尔米特型 最后，沃尔夫教授将研究 发展方程的能观能控性问题 关于黎曼流形上不变微分算子 齐性空间 群论基本上是对称性理论。 采取 一个简单的例子，当所讨论的系统在一个 空间原点位置的变化， 翻译自然会出现。 虽然组是抽象对象， 具体情况需要具体实现， 对称群的“表示”。

Professor Wolf will continue his research on Lie groups, harmonic analysis, and representation theory, with some applications to complex analysis, Riemannian geometry, and control theory. He will develop applications of his recent results on the equivalence of various methods of construction of representations. He will study the possibility of determining the character of a representation from a formula he has derived with R. Herb. He will complete his work on the Schwartz space of a general semisimple Lie group and study discrete series representations of groups of hermitian type. Finally, Professor Wolf will study the observability and controllability problems for evolution equations associated to invariant differential operators on Riemannian homogeneous spaces. Group theory is basically the theory of symmetry. To take a simple example, when the system in question is invariant under a change in the position of the origin of space, the group of translations naturally arises. While groups are abstract objects, particular situations demand concrete realizations or "representations" of the symmetry group.