We realize two families of combinatorial symmetric functions via the complex character theory of the finite general linear group ${\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_n({\mathbb{𝔽}}_q)$: chromatic quasisymmetric functions and vertical strip LLT polynomials. The associated ${\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_n({\mathbb{𝔽}}_q)$ characters are elementary in nature and can be obtained by induction from certain well-behaved characters of the unipotent upper triangular groups ${\mathrm{UT}<!--FUNCTION\; APPLICATION-->}_n({\mathbb{𝔽}}_q)$. 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 ${\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_n({\mathbb{𝔽}}_q)$ characters and Hessenberg varieties and a reinterpretation of known theorems and conjectures about the relevant symmetric functions in terms of ${\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_n({\mathbb{𝔽}}_q)$.

通过有限一般线性群的复特征理论实现了两族组合对称函数 ${\mathrm{GL}}_n({\mathbb{𝔽}}_q)$ ：色拟对称函数和垂直条 LLT 多项式。相关的 ${\mathrm{GL}}_n({\mathbb{𝔽}}_q)$ 特征本质上是基本的，可以通过单能上三角群的某些表现良好的特征归纳来获得 ${\mathrm{UT}}_n({\mathbb{𝔽}}_q)$ 。这些结果的证明还给出了计算归纳图的通用 Hopf 代数方法。其他结果包括相关之间的联系 ${\mathrm{GL}}_n({\mathbb{𝔽}}_q)$ 特征和 Hessenberg 簇，以及对有关对称函数的已知定理和猜想的重新解释 ${\mathrm{GL}}_n({\mathbb{𝔽}}_q)$ 。