V2EX macdonald polynomial

Macdonald Polynomial

Definition / 定义

Macdonald polynomial(麦克唐纳多项式):对称函数理论中的一类重要双参数(通常记为 \(q,t\))正交基(或基底)多项式/对称多项式族,统一并推广了多种经典对象,如 Schur 多项式、HallLittlewood 多项式、Jack 多项式等。常用于代数组合、表示论与数学物理中。

Pronunciation / 发音

/mk.d.nld pln.mi.l/

Examples / 例句

Macdonald polynomials depend on two parameters, \(q\) and \(t\).
麦克唐纳多项式依赖两个参数 \(q\) 和 \(t\)。

In algebraic combinatorics, Macdonald polynomials provide a unifying framework linking symmetric functions, representation theory, and \(q,t\)-statistics.
在代数组合中,麦克唐纳多项式提供了一个统一框架,把对称函数、表示论以及 \(q,t\) 统计量联系起来。

Etymology / 词源

该术语来自数学家 Ian G. Macdonald(伊恩G麦克唐纳)的姓氏;“polynomial”意为“多项式”。Macdonald 在对称函数与相关多项式体系的研究与整理中影响深远,因此这类多项式以其命名。

Related Words / 相关词

Literary Works / 著作示例

  • Symmetric Functions and Hall Polynomials(Ian G. Macdonald)
  • Orthogonal Polynomials Associated with Root Systems(I. G. Macdonald)
  • 相关研究论文中常见:关于 Macdonald 多项式的正交性、\(q,t\)-Kostka 系数、以及与根系/仿射 Hecke 代数的联系等主题
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