Geometry and the compression of combinatorial formulas for Macdonald polynomals

麦克唐纳多项式的几何和组合公式的压缩

• 批准号: 125974108
• 负责人: Professor Dr. Peter Littelmann
• 金额: --
• 依托单位: Abteilung Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/125974108?language=en
• 关键词: Geometry; compression; combinatorial; formulas; Macdonald

The aim of the project is to give a better understanding of the connection between the work of Gaussent, Littelmann, Schwer, Ram and Yip and the work of Haglund, Haiman and Loehr [3,4,5]. Both methods lead to rather different combinatorial formulas for Macdonald polynomials. It is expected that the connection between these formulas has a geometric background. The project has a geometric and a combinatorial part. The aim of the geometric part is to generalize the methods developed in [2] by Gaussent and Littelmann to a different class of Bott-Samelson varieties. The combinatorial part has as a goal to translate "geometry = counting points in a certain variety over a finite field with q elements" into a statistic on (generalized) Young diagrams producing a polynomial in q describing exactly the desired number.

该项目的目的是更好地理解Gaussent，Littelmann，Schwer，Ram和Yip的工作与Haglund，Haiman和Loehr的工作之间的联系[3，4，5]。这两种方法导致相当不同的组合公式麦克唐纳多项式。预计这些公式之间的联系具有几何背景。该项目有一个几何和组合的一部分。几何部分的目的是推广的方法在[2]中开发的Gaussent和Littelmann到一个不同的类的Bott-Samelson品种。组合部分的目标是将“几何=在具有q个元素的有限域上的某个种类中计数点”转化为（广义）杨氏图上的统计，从而在q中产生一个多项式，精确地描述所需的数量。