Mathematical Sciences: Dual Pair Correspondences Automorphic Forms and Hecke Algebras

数学科学：对偶对应自同构和赫克代数

• 批准号: 9623533
• 负责人: Gordan Savin
• 金额: $ 14.29万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623533&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dual; Pair; Correspondences

Abstract Savin 9623533 Savin will continue his work on exceptional dual pair correspondences, over p-adic and real fields, with applications to automorphic forms, in particular to the construction of a motive with Galois group G2. A purpose of this research is to get a better understanding of zeroes of polynomials. Almost everybody knows how to solve a quadratic equation. It is also possible, although it is less known, to find zeroes of any polynomial of degree 3 or 4. A higher degree polynomial, in general, can not be solved, but can be studied by attaching to it a mathematical object called the Galois group. Conversly, one can ask the following question: given a Galois group, can you find a polynomial corresponding to that group? The aim of this research is to give a positive answer to this question for a class of groups of type G2(p). The degrees of corresponding polynomials are, roughly speaking, the 6th power of the prime number p. For p=5 it is around 6 billion! This research will provide a good understanding of such polynomials.

抽象的Savin 9623533 Savin将继续他在P-ADIC和真实领域的杰出双对对应关系上继续他的工作，并应用于汽车形式，特别是使用Galois Group G2构建动机。 这项研究的目的是更好地了解多项式的零。几乎每个人都知道如何解决二次方程式。尽管鲜为人知，但也有可能找到第3度或4度多项式的零。通常无法解决较高的多项式，但可以通过将其附加到它上来研究一个称为Galois的数学对象团体。相反，人们可以提出以下问题：给定一个Galois组，您能找到与该组相对应的多项式吗？这项研究的目的是为一类G2（P）组给出一个积极的答案。 相应的多项式的程度大致说明了质子数p的第六功率。 对于p = 5，大约是60亿！ 这项研究将提供对此类多项式的良好理解。