Mathematical Sciences: Combinatorial Aspects of Representation Theory and the Theory of Symmetric Functions

数学科学：表示论和对称函数理论的组合方面

• 批准号: 9006413
• 负责人: Adriano Garsia
• 金额: $ 11.02万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006413&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Combinatorial; Aspects; Representation

This award supports the research in algebraic combinatorics of Professors Adriano Garsia and Jeffrey Remmel of the University of California at San Diego. They plan to develop combinatorial algorithms for the construction of representations and their decompositions into irreducible components. Among the specific topics they will work on are: the new Macdonald polynomials and their possible setting in representation theory; the structure of descent algebras of Coxeter groups; and the explicit evaluation of the coefficients in Schur function expansions in certain symmetric formal power series. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.

该奖项支持代数组合学的研究 Adriano Garsia和Jeffrey Remmel教授 位于圣地亚哥的加州。他们计划开发组合式的 表示及其构造的算法 分解成不可约的成分。在具体的 他们将工作的主题是：新的麦克唐纳多项式和 它们在表征理论中的可能设置; Coxeter群的下降代数;和显式求值 Schur函数展开式中的系数 对称形式幂级数 这项研究福尔斯属于广义的组合学范畴， 这是当今数学中最活跃的领域之一。 从根本上说，组合学代表了一个系统化的 首先是数学活动，计数在其 然而，现代的发展，组合学已经不仅仅是 计数利用各种先进的数学 技术，虽然它的根源可以追溯到几个世纪， 在过去的几十年里， 因为它在通信和信息方面的重要性， 技术.