AI 中文总结
研究晶体骨架相关内容，通过收缩准晶体得到晶体骨架并将其进一步平铺为准晶体骨架，刻画了相关边，收缩准晶体骨架组件产生布劳威尔序，还通过分析斯坦利对称函数展示了这些工具在对称函数中的应用。
AI 中文摘要
连通的\(\mathfrak{sl}_n\)-晶体的特征是舒尔多项式；该晶体可进一步分解为准晶体，其特征是盖塞尔拟对称函数。晶体骨架通过在晶体图内收缩准晶体得到。它推广了对偶等价图，当拟对称展开已知时可用于证明对称函数的舒尔展开。本文表明晶体骨架可进一步平铺成我们称为准晶体骨架的组件，其特征是杨拟对称舒尔函数。我们刻画了晶体骨架中在准晶体骨架组件之间移动的边。收缩准晶体骨架组件产生布劳威尔序。我们通过分析斯坦利对称函数来说明这些工具如何应用于对称函数。
英文摘要
The character of a connected $\mathfrak{sl}_n$-crystal is a Schur polynomial; the crystal can be further decomposed into quasicrystals, whose characters are the Gessel quasisymmetric functions. Crystal skeletons are obtained by contracting quasicrystals within crystal graphs. They generalize dual equivalence graphs, and can be used to prove the Schur expansion of a symmetric function when the quasisymmetric expansion is known. In this paper, we show that the crystal skeleton can be tiled further into components which we call quasicrystal skeletons, whose characters are Young quasisymmetric Schur functions. We characterize which edges in the crystal skeleton move between quasicrystal skeleton components. Contracting the quasicrystal skeleton components yields Bruhat order. We illustrate how these tools can be applied to symmetric functions by analyzing the Stanley symmetric functions.
Comments26 pages, 9 figures
