发表机构
Bucknell University（巴克内尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究SL(3,Z)的伊瓦同余子群I(3,p)的尖点上同调，推广相关经典结果，对p≤227的水平找到3个非零尖点类并计算两个水平的Hecke算子作用，得到伊瓦水平下的首个相关自守表示实例。
AI 中文摘要
我们研究SL(3,Z)的同余子群中在素数p处为伊瓦型的自守形式，具体考察伊瓦同余子群I(3,p)的尖点上同调，这类子群由SL(3,Z)中模p后为上三角的矩阵构成。为处理I(3,p)，我们推广了Ash、Grayson和Green在《J. Number Theory》1984年第19卷第412-436页的关键结果。对于p≤227的I(3,p)水平，我们发现三个具有非零尖点类的水平，并能计算其中两个水平的Hecke算子作用。这些是伊瓦水平下首次出现的、平凡上同调权且在p处为施泰因贝格型的非本质自对偶自守表示实例。
英文摘要
We investigate automorphic forms for congruence subgroups of $\mathrm{SL}(3, \mathbb{Z})$ that are Iwahori at $p$. In particular, we study the cuspidal cohomology of Iwahori congruence subgroups $\mathcal{I}(3, p)$, which are comprised of matrices in $\mathrm{SL}(3, \mathbb{Z})$ that are upper triangular modulo $p$. In order to work with $\mathcal{I}(3, p)$, we generalize key results from Ash, Grayson, and Green [J.\ Number Theory 19 (1984), pp.\ 412-436]. For levels $\mathcal{I}(3, p)$ with $p \leq 227$, we found three levels with nonzero cuspidal classes and were able to compute the action of Hecke operators at two of these levels. These are the first examples of non-essentially-self-dual automorphic representations of trivial cohomological weight that are Steinberg at $p$ appearing at Iwahori level.
Comments20 pages, 2 tables; comments welcome
