Mathematical Sciences: Research in Representation Theory andAutomorphic Forms

瓦拉赫教授将继续他在群体表征理论领域的研究。特别是他的研究将涉及库兹涅佐夫公式和拉普拉斯在局部对称空间上的推广。此外，他将在Toda格理论中研究Whittaker泛函的渐近行为，并在可约实约群的直接积分分解领域进行进一步的研究。群论基本上就是对称理论。举一个简单的例子，当所讨论的系统在空间原点位置的变化下是不变的，平移组自然产生。虽然群是抽象的对象，但特殊情况需要对称群的具体实现或“表示”。瓦拉赫教授的研究涉及具有几何或物理内容的群体的表示。

Professor Wallach will continue his research in the general area of group representation theory. In particular his research will involve a generalization of the Kuznetsov formula and the Laplacian on locally symmetric spaces. In addition he will study the asymptotic behavior of Whittaker functionals in the theory of the Toda lattice and further projects in the area of direct integral decompositions of reducible real reductive groups. 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. Professor Wallach's investigations involve representations of groups which have geometrical or physical content.