RUI: Mathematical Sciences: Spherical Characters on P-adic Coset Spaces and the Relative Trace Formula

RUI：数学科学：P-进陪集空间上的球面特征和相对迹公式

• 批准号: 9623125
• 负责人: Cary Rader
• 金额: $ 4.8万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623125&HistoricalAwards=false
• 关键词: RUI; Mathematical; Sciences; Spherical; Characters

Rader This award provides funding for a project in the Langlands program. The Relative Trace Formula (as initiated by Jacquet) is a new tool for studying automorphic L-functions and functoriality in the Langland's program. Rader and S. Rallis have been collaborating to prove some of the local results they think necessary to make the Relative Trace Formula a theorem instead of just a collection of examples. They have shown that many of the results known for usual character and central orbital integrals generalize to the case of spherical characters and double coset integrals on certain p-adic symmetric spaces. They plan to expand their research to include spherical subgroups such in the sense of M. Brion. Although it will take many years to complete such a project, it seems to be the natural domain for relative trace formulae, because (probably) one dimensional representations of H occur in irreducible smooth infinite dimensional representations of G with finite multiplicity. Rader also plans to complete a collaborative effort with Marie-France Vigneras investigating the geometric Zelevinskii involution for nilpotent orbits in certain Lie algebras. This should have applications in constructing modular representations of Hecke algebras, after Kazhdan-Lusztig. The Langlands program is part of number theory. Number theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished a driving force in creating new mathematics in other diverse parts of the discipline. The Langland's program is a general philosophy that connects number theory with calculus; it embodies the modern approach to the study of whole numbers. Modern number theory is very technical and deep, but it has had astonishing applications in areas like theoretical computer science and coding theory.

Rader这个奖项为Langlands计划项目提供了资金。相对痕量公式（由雅克（Jacquet）发起）是研究兰兰（Langland）计划中的自形L功能和功能性的新工具。 Rader和S. Rallis一直在合作，以证明他们认为将相对跟踪公式为Aorem而不仅仅是示例的集合所必需的一些本地结果。他们表明，许多以通常的特征和中央轨道积分已知的结果概括为球形字符的情况，并在某些P-ADIC对称空间上进行了双固定积分。他们计划扩大研究，以包括M. Brion的意义上的球形亚组。尽管完成这样的项目需要花费很多年，但它似乎是相对痕量公式的天然域，因为（可能）H的一个维度表示在不可还原的平滑光滑无限尺寸表示中，G的G具有有限的多样性。 Rader还计划与Marie-France Vigneras进行合作，调查了某些Lie代数中的Nilpotent Orbits的几何Zelevinskii。这应该在kazhdan-lusztig之后构建Hecke代数的模块化表示方面的应用。 兰兰兹计划是数字理论的一部分。数字理论是对整数的性质的研究，是数学最古老的分支。从一开始，理论的问题就为在学科的其他不同部分创建新数学方面提供了一种驱动力。兰兰（Langland）的计划是将数字理论与演算联系起来的一般哲学。 它体现了整个数字研究的现代方法。 现代数字理论非常技术性和深刻，但在理论计算机科学和编码理论等领域中具有惊人的应用。