Topics in representation theory and number theory

表示论和数论主题

• 批准号: 0901102
• 负责人: Benedict Gross
• 金额: $ 73.72万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901102&HistoricalAwards=false
• 关键词: Topics; representation; theory; number

"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)." Benedict Gross plans to do research on the boundary between representation theory and number theory, exploring the implications of the local and global Langlands correspondence. He expects to extend his conjectures with D. Prasad, on restriction from SO(n) to SO(n-1), to restriction problems for all classical groups. This will have implications for the arithmetic of Hermitian and orthogonal Shimura varieties. Gross also plans to investigate the simple supercuspidal representations he introduced with M. Reeder. He hopes to determine their wild Galois parameters in all cases, and to exploit their simple matrix coefficients in the trace formula.Benedict Gross plans to work on the boundary between questions in number theory, such as the representations of Galois groups, and questions in the representation theory of groups, such as the decomposition of the restriction of representations of the unitary group U(n) to the subgroup U(n-1). These problems are quite mysteriously related, via the conjectural Langlands correspondence, and Gross hopes to explore their connections in more detail.

“该裁决是根据2009年《美国复苏与再投资法》（公法111-5）资助的。”本尼迪克特总体计划对代表理论和数字理论之间的边界进行研究，并探讨了本地和全球兰兰人对应关系的含义。他希望在限制（n）到SO（n-1）的情况下，将他的猜想扩展到所有古典群体的限制问题。这将对Hermitian和正交Shimura品种的算术产生影响。 Gross还计划调查他与M. Reeder一起介绍的简单超级优势表示。他希望在所有情况下都确定其野生galois参数，并在痕量公式中利用其简单的矩阵系数。Beadict总体计划在数量理论中的问题之间进行边界工作，例如Galois群体的表示，以及在群体代表理论中的问题，例如分解了单位组U（N）的限制（n）u（n），以u（n）ucgorcouscouscouscon（n）u（n）。这些问题通过猜想的兰兰兹信函神秘地相关，而格罗斯希望更详细地探索它们的联系。