论文标题
异常分裂组的堕落Eisenstein系列和Siegel-Weil身份
Poles of degenerate Eisenstein series and Siegel-Weil identities for exceptional split groups
论文作者
论文摘要
令$ g $为线性分配代数组。在论文的第一部分中，研究了与最大抛物线子组$ e_ {p}（f^{0}，s，g）$相关的退化Eisenstein系列。在这一部分中，我们研究了区域中$ e_ {p}（f^{0}，s，g）$的杆子$ \ permatatorName {re} s> 0 $。我们确定劳伦（Laurent）扩展中的主要术语何时 $ e_ {p}（f^{0}，s，g）$周围$ s = s_0 $是正方形的。第二部分致力于在不同点的各个Eisenstein系列的领先术语之间找到身份。我们提出了一种算法来查找此数据并在\ textit {sage}上实现它。尽管这两个零件都可以应用于一般代数组，但我们将自己限制在$ g $类型$ f_4，e_6，e_7 $的情况下，并获得新的结果。
Let $G$ be a linear split algebraic group. The degenerate Eisenstein series associated to a maximal parabolic subgroup $E_{P}(f^{0},s,g)$ with the spherical section $f^{0}$ is studied in the first part of the thesis. In this part, we study the poles of $E_{P}(f^{0},s,g)$ in the region $\operatorname{Re} s >0$. We determine when the leading term in the Laurent expansion of $E_{P}(f^{0},s,g)$ around $s=s_0$ is square integrable. The second part is devoted to finding identities between the leading terms of various Eisenstein series at different points. We present an algorithm to find this data and implement it on \textit{SAGE}. While both parts can be applied to a general algebraic group, we restrict ourself to the case where $G$ is split exceptional group of type $F_4,E_6,E_7$, and obtain new results.
