论文标题
a $ \ mathrm {gl}（\ mathbb {f} _q）$ - 兼容unitriangular类功能的兼容hopf代数
A $\mathrm{GL}(\mathbb{F}_q)$-compatible Hopf algebra of unitriangular class functions
论文作者
论文摘要
本文构造了一个新颖的Hopf代数$ \ MATHSF {CF}（\ Mathrm {ut} _ {\ bullet}）$上的单位上三角形组$ \ mathrm {ut} _ {n}（n}（n}）（\ Mathbb {f} finite finitiate）的类函数。这种结构本质上是代表性的理论，并在矢量物种类别中使用了Hopf Monoid的机械。与类似的已知结构相反，该HOPF代数具有诱导有限的通用线性组的特性，引起了$ \ Mathrm {gl} _ {n}的Zelevinsky的Hopf代数的同态性，（\ Mathbb {f} _ {q} _ {q} _ {q} _ {q}）此外，$ \ MATHSF {CF}（\ Mathrm {ut} _ {\ bullet}）$包含一个hopf subalgebra，该subalgebra对以前用于证明有关copture的quaSianture quasisasiSymmetric函数是同构的。还建立了一些HOPF代数属性。
This paper constructs a novel Hopf algebra $\mathsf{cf}(\mathrm{UT}_{\bullet})$ on the class functions of the unipotent upper triangular groups $\mathrm{UT}_{n}(\mathbb{F}_{q})$ over a finite field. This construction is representation theoretic in nature and uses the machinery of Hopf monoids in the category of vector species. In contrast with a similar known construction, this Hopf algebra has the property that induction to the finite general linear group induces a homomorphism to Zelevinsky's Hopf algebra of $\mathrm{GL}_{n}(\mathbb{F}_{q})$ class functions. Furthermore, $\mathsf{cf}(\mathrm{UT}_{\bullet})$ contains a Hopf subalgebra which is isomorphic to a known combiantorial Hopf algebra, previously used to prove a conjecture about chromatic quasisymmetric functions. Some additional Hopf algebraic properties are also established.
