论文标题
小伍德 - 里查森（Littlewood-Richardson）的koornwinder多项式规则
A Littlewood-Richardson rule for Koornwinder polynomials
论文作者
论文摘要
Koornwinder多项式是$ Q $ - 接地多项式，配备了额外的五个参数和$ b C_N $ -Type Weyl grout Symmetry，这是由Koornwinder（1992）作为Askey-Wilson polynomials的多元类似物引入的。现在，它们被理解为与$（c^\ vee_n，c_n）$ offine root系统相关的麦克唐纳（MacDonald）多项式，这是通过麦克唐纳德·奇德尼克（MacDonald-Cherednik）的双偏爱hecke代数的理论。在本文中，我们给出了Koornwinder多项式的Littlewood-Richardson系数的明确公式，即产品的结构常数为不变多项式。我们的公式是天然的$（c^\ vee_n，c_n）$ - YIP的Alcove-Walk-Walk-walk公式（2012）的类似物，在减少仿射根系的情况下给出了。
Koornwinder polynomials are $q$-orthogonal polynomials equipped with extra five parameters and the $B C_n$-type Weyl group symmetry, which were introduced by Koornwinder (1992) as multivariate analogue of Askey-Wilson polynomials. They are now understood as the Macdonald polynomials associated to the affine root system of type $(C^\vee_n,C_n)$ via the Macdonald-Cherednik theory of double affine Hecke algebras. In this paper we give explicit formulas of Littlewood-Richardson coefficients for Koornwinder polynomials, i.e., the structure constants of the product as invariant polynomials. Our formulas are natural $(C^\vee_n,C_n)$-analogue of Yip's alcove-walk formulas (2012) which were given in the case of reduced affine root systems.
