论文标题
$ sl_2的某些复杂表示（\ bar {\ mathbb {f}} _ q）$
Certain complex representations of $SL_2(\bar{\mathbb{F}}_q)$
论文作者
论文摘要
我们为连接的还原式代数组$ {\ bf g} $介绍了表示类别$ \ mathscr {c}（{\ bf g}）$，该$ {\ bf g} $，该$ {\ bf g} $在有限的字段$ \ mathbb {f} _q $ q $ q $ elements上定义。我们表明，此类别具有$ {\ bf g} = sl_2（\ bar {\ mathbb {f}} _ q）$的许多良好属性。特别是，它是Abelian类别，也是最高权重类别。此外，我们将简单对象分类为$ \ Mathscr {c}（{\ bf g}）$ for $ {\ bf g} = sl_2（\ bar {\ bar {\ mathbb {f}} _ q）$。
We introduce the representation category $\mathscr{C}({\bf G})$ for a connected reductive algebraic group ${\bf G}$ which is defined over a finite field $\mathbb{F}_q$ of $q$ elements. We show that this category has many good properties for ${\bf G}=SL_2(\bar{\mathbb{F}}_q)$. In particular, it is an abelian category and a highest weight category. Moreover, we classify the simple objects in $\mathscr{C}({\bf G})$ for ${\bf G}=SL_2(\bar{\mathbb{F}}_q)$.
