Mathematical Sciences: Generalized Selberg-Jack Symmetric Functions and Constant Term Identities

数学科学：广义 Selberg-Jack 对称函数和常数项恒等式

• 批准号: 9002043
• 负责人: Kevin Kadell
• 金额: $ 4.04万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002043&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Generalized; Selberg; Jack

A central goal of this mathematical research is the use of newly developed relationships between special functions applied to the evaluation of complex integrals. The primary focus is that of the famous Selberg formula for the integration of symmetric functions multiplied against the Vandermonde determinant, acting as a weight. Work will continue addressing possible extensions of this closed form expression. Initial efforts will be made to establish a formula for the ratios of alternantes to the Selberg symmetric functions. It is expected that they will be given explicitly in terms of tournaments. Work will also be done on beta type distributions and their orthogonal polynomials. In addition, the classification of functions which provide extensions of the q- Dyson theorem of Zeilberger and Bressoud will be sought. It is conjectured that not all such functions will turn out to be symmetric.

这个数学研究的中心目标是利用新发展的特殊函数之间的关系来计算复积分。主要的焦点是著名的塞尔伯格公式，用于对称函数的积分乘以范德蒙德行列式，作为一个权重。工作将继续解决这种封闭形式表达式的可能扩展。初步的努力将建立一个公式的比率的交替Selberg对称函数。预计他们将在比赛中明确给出。我们还将研究β型分布及其正交多项式。此外，将寻求提供Zeilberger和Bressoud的q- Dyson定理扩展的函数的分类。据推测，并非所有这样的函数都是对称的。