Applications of quasisymmetric schur functions

拟对称 schur 函数的应用

• 批准号: 251350-2010
• 负责人: VanWilligenburg, Stephanie
• 金额: $ 1.75万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=479676
• 关键词: Applications; quasisymmetric; schur; functions

Quasisymmetric functions arise in a number of areas of mathematics. For example, in discrete geometry they arise as weight enumerators for labelled partially ordered sets, and generate specific well known functions such as skew Schur functions, and Stanley symmetric functions. Meanwhile in the arena of category theory they are the terminal object in the category of combinatorial Hopf algebras equipped with a zeta function. With regard to combinatorial probability they arise in the study of random permutations with respect to a certain distribution. They also arise in representation theory as characters of a degenerate quantum group. Consequently a deep understanding of quasisymmetric functions is important as knowledge about them will impact each of the above areas, plus other areas in which they arise.

拟对称函数出现在许多数学领域中。例如，在离散几何中，它们作为标记部分有序集的权重枚举器出现，并生成特定的众所周知的函数，例如偏斜舒尔函数和斯坦利对称函数。同时，在范畴论领域，它们是配备 zeta 函数的组合 Hopf 代数范畴中的终端对象。关于组合概率，它们出现在对特定分布的随机排列的研究中。它们也在表示论中作为简并量子群的特征出现。因此，对拟对称函数的深入理解非常重要，因为有关它们的知识将影响上述每个领域以及它们出现的其他领域。