Mathematical Sciences: Invariant Distributions on Reductive Groups

9400797 Herb Herb将继续她在表示理论和关于约化p-进群的调和分析领域的工作。她将集中研究这些群上最重要的不变量分布，即回火特征标和轨道积分。她感兴趣的具体问题包括计算轨道积分的傅里叶逆公式，以及研究非连通群的诱导表示的可约性。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。***

9400797 Herb Herb will continue her work in the field of representation theory and harmonic analysis on reductive p-adic groups. She will concentrate on studying the most important invariant distributions on these groups, namely tempered characters and orbital integrals. Specific problems which she is interested in include computing Fourier inversion formulas for orbital integrals, and studying reducibility of induced representations for non connected groups. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics. ***