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.

“该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。本尼迪克特·格罗斯计划研究表示论和数论之间的界限，探索局部和全局朗兰兹对应的含义。他希望能与D.普拉萨德，限制从SO（n）到SO（n-1），限制问题的所有经典群体。这将对Hermitian和正交Shimura簇的算术产生影响。格罗斯还计划研究他与M.里德。他希望确定他们的野生伽罗瓦参数在所有情况下，并利用其简单的矩阵系数的痕迹formulation.Benedict格罗斯计划工作之间的边界问题在数论，如代表伽罗瓦群体，和问题的代表理论的群体，如分解的限制表示的酉群U（n）的子群U（n-1）。这些问题是相当神秘的相关，通过学术朗兰兹对应，格罗斯希望探索他们的联系更详细。