维数不超过$\ell^4$的有限李型典型群表示分类
Classifying representations of finite classical groups of Lie type of dimension up to $\ell^4$
AI总结：
本文针对特征p>2的域上秩为ℓ的有限李型典型群，分类维数不超过ℓ⁴的不可约表示，给出维数计算显式公式，相关结果可支撑伽罗瓦表示领域经典问题研究。
摘要：
设$G$是定义在特征$p>2$的域上、秩为$\ell$的有限李型典型群。本研究对$G$的维数以与$\ell$成正比的常数为上界的不可约表示进行分类，依据$G$是否为$A_\ell$型分为两类情况讨论。此外，我们探讨了计算此类表示维数的显式公式。本工作的部分动机源于希望获得关于伽罗瓦表示的两个经典问题的新结果：自守伽罗瓦表示的大像猜想以及逆伽罗瓦问题。本文最后就这些研究方向的潜在影响给出了若干评述。
英文摘要：
Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to $\ell$, and splits into two cases according to $G$ is of type $A_{\ell}$ or not. Furthermore, we discuss explicit formulas for computing the dimensions of such representations. The motivation for this work arises, in part, from a desire to obtain new results on two classical problems concerning Galois representations: the large image conjecture for automorphic Galois representations and the inverse Galois problem. We conclude the paper by giving some remarks on potential implications in these addresses.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
