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: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=525103
• 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.

准对称函数出现在许多数学领域。例如，在离散几何中，它们作为标记的偏序集的权重枚举数出现，并生成特定的众所周知的函数，如Skew Schur函数和Stanley对称函数。同时，在范畴理论中，它们是赋Zeta函数的组合Hopf代数范畴的终端对象。关于组合概率，它们出现在关于某一分布的随机排列的研究中。它们也出现在表象理论中，作为简并量子群的特征。因此，对准对称函数的深入理解是重要的，因为关于它们的知识将影响到上述每个领域，以及它们产生的其他领域。