论文标题
有限图案组的表示
Representations of finite pattern groups
论文作者
论文摘要
令$ g = 1+a $是有限字段$ {\ mathbb {f}} _ q $上的有限模式组。我们在$ g $的共同连接轨道及其等效类别的不可约合表示之间进行自然培养。更准确地说，在A^t $中给定任何$ t \，被视为相关的coadjoint轨道$ {\ mathfrak {\ mathfrak {o}} _ t $ $ g $的_ t $，我们可以明确地构建一个$ g $的子group $ h_t $ g $，例如$ {\ mathrm {ind}} _ {h_t}^gψ_t\ cong {\ mathrm {indrm {ind}} _ {这里$
Let $G=1+A$ be a finite pattern group over the finite field ${\mathbb{F}}_q$. We give a natural bijection between coadjoint orbits of $G$ and its equivalent classes of irreducible representations. More precisely, given any $T\in A^t$, viewed as a representative of associated coadjoint orbit ${\mathfrak{O}}_T$ of $G$, we can explicitly construct a subgroup $H_T $ of $G$, such that ${\mathrm{Ind}}_{H_T}^G ψ_T$ is irreducible and ${\mathrm{Ind}}_{H_T}^G ψ_T \cong {\mathrm{Ind}}_{H_{T'}}^G ψ_{T'}$ if and only if $T$ and $ T'$ are in the same coadjoint orbit. Here $ψ_T(x)=ψ({\mathrm{tr}} Tx)\text{ for }x\in H_T,$ and $ψ$ is a fixed nontrivial additive character of ${\mathbb{F}}_q$.
