The Stembridge equality for skew stable Grothendieck polynomials and skew dual stable Grothendieck polynomials
The Stembridge equality for skew stable Grothendieck polynomials and skew dual stable Grothendieck polynomials
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偏斜稳定格罗腾迪克多项式和偏斜双稳定格罗腾迪克多项式的 Stembridge 等式
DOI：
10.5802/alco.199
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发表时间：
2021
影响因子：
--
通讯作者：
Jakin Ng
中科院分区：
文献类型：
--
作者：
Fiona Abney;S. An;Jakin Ng
Schur多项式s λ是理解一般线性群的表示理论的必要条件。它们也描述了格拉斯曼环的上同调环。对于ρ =（n，n − 1，.，1)一个阶梯形状和μ ρ ρ一个子分区，Stembridge等式表明s ρ/μ = s ρ/μ T。这个等式提供了关于上同调环对称性的信息。稳定的格罗滕迪克多项式G λ和对偶稳定的格罗滕迪克多项式g λ，由Buch、Lam和Pylyavskyy提出，是舒尔多项式的变体，描述了格拉斯曼的K -理论。利用对称函数环的Hopf代数结构和推广的Littlewood-Richardson规则，我们证明了G ρ/μ = G ρ/μ T和g ρ/μ = g ρ/μ T，它们是斜稳定和斜对偶稳定Grothendieck多项式的Stembridge等式的类似.
The Schur polynomials s λ are essential in understanding the representation theory of the general linear group. They also describe the cohomology ring of the Grassmannians. For ρ = ( n,n − 1 ,..., 1) a staircase shape and µ ⊆ ρ a subpartition, the Stembridge equality states that s ρ/µ = s ρ/µ T . This equality provides information about the symmetry of the cohomology ring. The stable Grothendieck polynomials G λ , and the dual stable Grothendieck polynomials g λ , developed by Buch, Lam, and Pylyavskyy, are variants of the Schur polynomials and describe the K -theory of the Grassmannians. Using the Hopf algebra structure of the ring of symmetric functions and a generalized Littlewood–Richardson rule, we prove that G ρ/µ = G ρ/µ T and g ρ/µ = g ρ/µ T , the analogues of the Stembridge equality for the skew stable and skew dual stable Grothendieck polynomials.