论文标题
有限符号和统一组的指数总和和总威尔表示
Exponential sums and total Weil representations of finite symplectic and unitary groups
论文作者
论文摘要
我们在特征性的$ p> 2 $中构建明确的本地系统，其几何单型组是所有$ n \ ge 2 $的有限符号组$ sp_ {2n}（q）$，而其他人的几何n \ ge 2 $则是特殊的unitary unitary groups $ su_n（q）$ su_n（q）$ n odd $ n $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q。这些本地系统的一个主要优点是它们相关的痕量功能是一个参数属于一个非常简单（即易于记住的形式）的指数总和。我们还在$ g_m $上表现出超几何滑轮，其几何单型组是任何$ n \ ge 2 $的有限符号组$ sp_ {2n}（q）$，而其他的几何单型单型组是有限的一般unital unital $ gu_n（q）$ gu_n（q）$ nodd $ n odd $ n $ n \ geq geq 3 $。
We construct explicit local systems on the affine line in characteristic $p>2$, whose geometric monodromy groups are the finite symplectic groups $Sp_{2n}(q)$ for all $n \ge 2$, and others whose geometric monodromy groups are the special unitary groups $SU_n(q)$ for all odd $n \ge 3$, and $q$ any power of $p$, in their total Weil representations. One principal merit of these local systems is that their associated trace functions are one-parameter families of exponential sums of a very simple, i.e., easy to remember, form. We also exhibit hypergeometric sheaves on $G_m$, whose geometric monodromy groups are the finite symplectic groups $Sp_{2n}(q)$ for any $n \ge 2$, and others whose geometric monodromy groups are the finite general unitary groups $GU_n(q)$ for any odd $n \geq 3$.
