Mathematical Sciences: Unitary Representations of ReductiveReal Lie Groups and Derived Functor Modules

数学科学：还原实李群和派生函子模的酉表示

• 批准号: 9108990
• 负责人: Susana Salamanca-Riba
• 金额: $ 3.33万
• 依托单位: New Mexico State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9108990&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Unitary; Representations; ReductiveReal

Professor Salamanca Riba will investigate various topics in the theory of unitary representations of reductive Lie groups. Firstly, she will attempt to complete a proof of a conjecture of Zuckerman that certain Harish-Chandra modules are isomorphic to Zuckerman functor modules. In addition she will consider other generalizations of the above conjecture. For example, in certain cases Barbasch and Vogan have conjectured that these derived functor modules are obtained from a special unipotent representation. Professor Salamanca Riba will attempt to prove this. The research project being described here is in group representation theory. Groups usually arise as transformations which preserve the structure of a system under investigation, as for example the group of rotations around the center preserves a sphere. In specific applications a concrete realization of the abstract group, or representation, is often needed. These are the objects which are being studied here.

萨拉曼卡·里巴教授将研究各种主题， 约化李群的酉表示理论。 首先，她将尝试完成一个猜想的证明， Zuckerman证明了某些Harish-Chandra模同构于 Zuckerman函子模 此外，她还将考虑其他 上述猜想的推广。例如在某些 案例Barbasch和Vogan已经证实，这些衍生 函子模是从一个特殊的幂幺元得到的 表示. 萨拉曼卡·里巴教授将试图证明 这个 这里所描述的研究项目是在小组 表征理论 群通常作为变换而出现 它保留了被调查系统的结构， 例如，围绕中心的旋转组保持 球体。 在具体应用中， 通常需要抽象组或表示。 这些都是 这里正在研究的对象。