论文标题
单细胞LLT多项式和常规半神经赫森伯格品种的双胞胎
Unicellular LLT polynomials and twin of regular semisimple Hessenberg varieties
论文作者
论文摘要
Brosnan-Chow的Shareshian-Wachs猜想的解决方案将常规半神经Hessenberg品种的共同学和单位间隔图上的分级色对称函数联系起来。另一方面，众所周知，单细胞LLT多项式具有与分级色的对称函数相似的特性。在本文中，我们将Ayzenberg-Buchstaber引入的普通半岛Hessenberg品种的单细胞LLT多项式链接在一起。我们从拓扑角度证明了它们的回文。我们还表明，由置换ho的面孔产生的对称群体的模块与移动的单细胞LLT多项式有关，并观察转移的单细胞LLT多项式的$ e $ e $ - 积极性，这是由Alexandersson-Sulzgruber在Path Graphs和Contrapical Conegipts和COHOM上通过Alexandersson-Sulzgruber确定的。
The solution of Shareshian-Wachs conjecture by Brosnan-Chow linked together the cohomology of regular semisimple Hessenberg varieties and graded chromatic symmetric functions on unit interval graphs. On the other hand, it is known that unicellular LLT polynomials have similar properties to graded chromatic symmetric functions. In this paper, we link together the unicellular LLT polynomials and twin of regular semisimple Hessenberg varieties introduced by Ayzenberg-Buchstaber. We prove their palindromicity from topological viewpoint. We also show that modules of a symmetric group generated by faces of a permutohedron are related to a shifted unicellular LLT polynomial and observe the $e$-positivity of shifted unicellular LLT polynomials, which is established by Alexandersson-Sulzgruber in general, for path graphs and complete graphs through the cohomology of the twins.
