论文标题
基因组Schur函数的弱Bruhat间隔模块
Weak Bruhat interval modules for genomic Schur functions
论文作者
论文摘要
令$λ$为正整数$ n $的分区。基因组Schur函数$u_λ$是由Pechenik引入的 - Yong在$ k $ - 格拉曼尼亚人理论的背景下。最近，Pechenik在增加无间隙tableaux方面提供了$U_λ$的基本准对称扩展的正组合公式。 In this paper, for each $1 \le m \le n$, we construct an $H_m(0)$-module $\mathbf{G}_{λ;m}$ whose image under the quasisymmetric characteristic is the $m$th degree homogeneous component of $U_λ$ by defining an $H_m(0)$-action on increasing gapless tableaux.我们提供了一种将置换分配给每个增加的无间隙图表的方法，并使用此分配将$ \ mathbf {g} _ {λ; m} $分解为弱bruhat间隔模块的直接总和。此外，我们确定直接总和分解的每个汇总的投影覆盖。
Let $λ$ be a partition of a positive integer $n$. The genomic Schur function $U_λ$ was introduced by Pechenik--Yong in the context of the $K$-theory of Grassmannians. Recently, Pechenik provided a positive combinatorial formula for the fundamental quasisymmetric expansion of $U_λ$ in terms of increasing gapless tableaux. In this paper, for each $1 \le m \le n$, we construct an $H_m(0)$-module $\mathbf{G}_{λ;m}$ whose image under the quasisymmetric characteristic is the $m$th degree homogeneous component of $U_λ$ by defining an $H_m(0)$-action on increasing gapless tableaux. We provide a method to assign a permutation to each increasing gapless tableau, and use this assignment to decompose $\mathbf{G}_{λ;m}$ into a direct sum of weak Bruhat interval modules. Furthermore, we determine the projective cover of each summand of the direct sum decomposition.
