Atlas of Lie Groups and Representations

线性约化群的表示论，如GL（n）是一个非常活跃的学科，部分原因是它在自守形式和朗兰兹纲领中的应用。然而，重要的有趣的例子自守形式来自非线性群，即群p不能实现为一个子群的GL（n）。一个基本结果，理论的真实的还原群是沃根对偶。在与Peter Trapa的合作中，我计划将其扩展到非线性群体。有一些有趣的功能，在这种设置是完全不同的线性case.In一个联合项目与丽贝卡赫伯我建议研究字符的真实的还原非线性群体，通过将它们与线性群体通过“提升”理论。这种提升是密切相关的沃根对偶为这些群体。在一个项目与Niranjan Ramachandran我正在研究的结构非线性p-adic约化群。这是研究这些群的特征标理论的重要的第一步。最后，我和Angret Paul正在进行一个项目，尽可能完整地参数化一维表示的R上的θ-对应。

The representation theory of linear reductive groups, such as GL(n) is a very active subject, in part because of applications to the automorphic forms and the Langlands program. However important interesting examples of automorphic forms come from non-linear groups, i.e. groups pwhich can not be realized as a subgroup of GL(n).A fundamental result in the theory of real reductive groups is Vogan duality. In joint work with Peter Trapa I plan to extend this to non-linear groups. There are a number of interesting features in this setting which are quite different from the linear case.In a joint project with Rebecca Herb I propose to study the characters of real reductive non-linear groups, by relating them to linear groups via a "lifting" theory. This lifting is closely related to Vogan duality for these groups.In a project with Niranjan Ramachandran I am studying the structure of non-linear p-adic reductive groups. This is an important first step in studying character theory for these groups.Finally Annegret Paul and I are working on a project to parametrize the theta-correspondence over R for one-dimensional representations as completely as possible.