In this article, several cohomology spaces associated to the arithmetic groups $\mr{SL}_3(\Z)$ and $\mr{GL}_3(\Z)$ with coefficients in any highest weight representation $\m_\lambda$ have been computed, where $\lambda$ denotes their highest weight. Consequently, we obtain detailed information of their Eisenstein cohomology with coefficients in $\m_\lambda$. When $\m_\lambda$ is not self dual, the Eisenstein cohomology coincides with the cohomology of the underlying arithmetic group with coefficients in $\m_\lambda$. In particular, for such a large class of representations we can explicitly describe the cohomology of these two arithmetic groups. We accomplish this by studying the cohomology of the boundary of the Borel-Serre compactification and their Euler characteristic with coefficients in $\m_\lambda$. At the end, we employ our study to discuss the existence of ghost classes.

中文翻译：

---

$$\mathrm {SL}_3({\mathbb {Z}})$$SL3(Z)的边界和爱森斯坦上同调

在本文中，几个与算术群 $\mr{SL}_3(\Z)$ 和 $\mr{GL}_3(\Z)$ 相关的上同调空间，其系数在任何最高权重表示 $\m_\lambda$已计算，其中 $\lambda$ 表示它们的最高权重。因此，我们获得了其系数为 $\m_\lambda$ 的 Eisenstein 上同调的详细信息。当 $\m_\lambda$ 不是自对偶时，Eisenstein 上同调与系数在 $\m_\lambda$ 中的基础算术群的上同调一致。特别是，对于如此大的一类表示，我们可以明确地描述这两个算术群的上同调。我们通过研究 Borel-Serre 紧化边界的上同调及其系数为 $\m_\lambda$ 的欧拉特征来实现这一点。在最后，