论文标题
彩色准对称函数的一项实现
A unipotent realization of the chromatic quasisymmetric function
论文作者
论文摘要
本文通过有限的通用线性组$ \ mathrm {gl} _ {n}（\ Mathbb {f} _ {q}）$：彩色准对象函数和垂直条带llt polynomials来实现两个组合对称函数的家族。关联的$ \ mathrm {gl} _ {n}（\ mathbb {f} _ {q}）$字符本质上是基本的，可以从单位上三角形上三角形的某些良好性的字符中获得诱导，从而获得了诱导，这些结果的证明还提供了一种一般的HOPF代数方法来计算归纳图。其他结果包括相关$ \ mathrm {gl} _ {n}（\ Mathbb {f} _ {q}）$字符和Hessenberg品种之间的联系$ \ mathrm {gl} _ {n}（\ mathbb {f} _ {q}）$。
This paper realizes of two families of combinatorial symmetric functions via the complex character theory of the finite general linear group $\mathrm{GL}_{n}(\mathbb{F}_{q})$: chromatic quasisymmetric functions and vertical strip LLT polynomials. The associated $\mathrm{GL}_{n}(\mathbb{F}_{q})$ characters are elementary in nature and can be obtained by induction from certain well-behaved characters of the unipotent upper triangular groups $\mathrm{UT}_{n}(\mathbb{F}_{q})$. The proof of these results also gives a general Hopf algebraic approach to computing the induction map. Additional results include a connection between the relevant $\mathrm{GL}_{n}(\mathbb{F}_{q})$ characters and Hessenberg varieties and a re-interpretation of known theorems and conjectures about the relevant symmetric functions in terms of $\mathrm{GL}_{n}(\mathbb{F}_{q})$.
