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.

“该奖项的资金来源是《2009 年美国复苏和再投资法案》（公法 111-5）。”本尼迪克特·格罗斯计划研究表示论和数论之间的边界，探索局部和全球朗兰兹对应的含义。他希望将他与 D. Prasad 的关于从 SO(n) 到 SO(n-1) 的限制的猜想扩展到所有经典群的限制问题。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. Reeder 一起引入的简单超尖峰表示。他希望在所有情况下确定它们的狂野伽罗瓦参数，并在迹公式中利用它们的简单矩阵系数。本尼迪克特·格罗斯计划研究数论中的问题（例如伽罗瓦群的表示）和数学中的问题之间的边界。群的表示理论，例如将酉群 U(n) 的表示限制分解为子群 U(n-1)。通过推测的朗兰兹对应关系，这些问题之间存在着相当神秘的联系，格罗斯希望更详细地探索它们之间的联系。