Mathematical Sciences: Permutation Representations, Monodromy and Matrix Classes

数学科学：排列表示、单向性和矩阵类

• 批准号: 9300660
• 负责人: Robert Guralnick
• 金额: $ 7.74万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9300660&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Permutation; Representations; Monodromy

This award supports research in two areas. First the principal investigator will study permutation representations. He will classify all monodromy groups of primitive branched coverings of Riemann surfaces which are sufficiently large in terms of the genus. He will also consider similar problems over finite fields and their algebraic closures, and over number fields. In addition, he will consider problems involving nonconjugate subgroups which induce the same permutation representation. The second major area of investigation is matrix theory. In particular, the principal investigator will determine what can be said about the minimal polynomial of a symmetric matrix over the integers. He also intends to investigate the structure of the variety of commuting r-tuples of matrices. A group is an algebraic structure with a single operation. It appears in many areas of mathematics, as well as, physics and chemistry. The fundamental building blocks of finite groups are finite simple groups. One of the major results in mathematics of the past decade is the classification of the finite simple groups, the proof of which would require 10,000 to 15,000 journal pages. This research is aimed at using this classification in the study of arbitrary finite groups and other algebraic structures.

该奖项支持两个领域的研究。 首先 主要研究者将研究排列表示。 他将把原始分枝的所有单值群 覆盖的黎曼曲面，这是足够大， 属的术语。 他也会考虑类似的问题， 有限域和它们的代数闭包，以及 领域的 此外，他还将考虑以下问题： 诱导相同置换的非共轭子群 表示. 第二个主要的调查领域是矩阵 理论 特别是，主要研究者将确定 关于对称的最小多项式， 矩阵的整数。 他还打算调查 矩阵的交换r元组的多样性的结构。 一个群是一个具有单一运算的代数结构。 它出现在数学的许多领域，以及，物理学和 化学. 有限群的基本构造块是 有限单群 数学中的一个重要成果是 过去的十年是有限简单的分类 团体，这将需要10，000至15，000的证明 日记页。 这项研究旨在利用这一 分类在任意有限群的研究和其他 代数结构