Bruht-Tits Buildings and the Representation Theory of a Reductive P-adic Group

Bruht-Tits 大厦与还原 P-adic 群的表示论

• 批准号: 0100413
• 负责人: Allen Moy
• 金额: $ 24.82万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100413&HistoricalAwards=false
• 关键词: Bruht; Tits; Buildings; Representation; Theory

AbstractMoyMoy will investigate two topics in the representation theory of reductive p-adic groups. In the first project, Moy will study the use of the Bruhat-Tits building of a reductive group in its representation theory and harmonic analysis. Moy will investigate by two different methods the very old fundamental conjecture that every irreducible supercuspidal representation is compactly induced from an open compact modulo center subgroup. The first of these two methods is based upon extension of earlier joint work of Moy and Prasad which proved the conjecture in the case the supercuspidal representation has depth zero. The second method would be to show that any irreducible smooth representation which does not contain a cuspidal representation of a parahoric subgroup must have a nonzero Jacquet functor. Both these methods involve the Bruhat-Tits building. Also as part of the first project, Moy will extend his joint work with Barbasch which gave a new proof of the Howe conjecture on orbital integrals to other twisted cases. For the second project, Moy will investigate explicit construction of G-invariant essentially compact distributions on the group G.

摘要MoyMoy将研究约化p-adic群的表示论中的两个主题。 在第一个项目中，Moy将研究在其表示理论和调和分析中使用Bruhat-Tits构建还原群。 莫伊将调查由两种不同的方法非常古老的基本猜想，每一个不可约超尖点表示是compensately诱导从一个开放的紧凑模中心子群。 这两种方法中的第一种是基于Moy和Prasad早期联合工作的扩展，该工作证明了超尖点表示深度为零的情况下的猜想。 第二种方法是证明任何不包含一个parahoric子群的尖点表示的不可约光滑表示必须有一个非零的Jacquet函子。 这两种方法都涉及布鲁哈特-山雀建筑。 此外，作为第一个项目的一部分，莫伊将延长他的联合工作与Barbasch这给了一个新的证明豪猜想轨道积分的其他扭曲的情况下。 在第二个项目中，Moy将研究群G上G-不变本质紧分布的显式构造。