Mathematical Sciences: Representation Theory of Reductive Groups

本研究项目属于表征领域 理论和调和分析， 其他reductive algebraic groups 首席研究员亚当斯 将继续研究亚瑟的预言和 真实的群体的表示。 此外，亚当斯的研究将 研究了L-群在还原对偶中的作用， 对，都为真实的群体，并在有限和p-adic领域。 赫伯调查员将继续她对施瓦茨空间的研究 对于具有无穷中心的半单李群。 这些问题 需要展示波包如何在 不同系列的调和表示重叠。 而且这 研究涉及到对超调和表象的检验 在p-轨道积分的傅立叶反演的背景下， adic群 这项研究属于现代分析的一般领域， 特别是，在获得的表示群的 空间上的变换。

This research project is in the field of representation theory and harmonic analysis on real reductive Lie groups and other reductive algebraic groups. Principal investigator Adams will continue his study of Arthur's conjectures and unipotent representations for real groups. Also, Adams' research will involve an examination of the role of L-groups in reductive dual pairs, both for real groups, and over finite and p-adic fields. Investigator Herb will continue her study of the Schwarz space for semisimple Lie groups with infinite center. These problems require showing how wave packets patch together at points where different series of tempered representations overlap. Also, this research involves an examination of supertempered representations in the context of Fourier inversion of orbital integrals for p- adic groups. This research is in the general area of modern analysis and, in particular, in obtaining the representations of groups of transformations on spaces.