论文标题
SL（3，Z）的同时学，具有标准表示的系数
Cohomology of SL(3,Z) with coefficients in the standard representation
论文作者
论文摘要
本文是与Bajpai，Harder和Moya Giusti \ Cite {BHHM}的联合论文的自然延续，即使它开始是对Goncharov问题的答案。在那篇论文中，除了奇怪的对称能力及其双重能力外，我们对所有表示形式都有完整的描述。对于这些表示形式，我们有两个选择：某些一维模块是鬼空间。在这里，我们发现$ h^2（sl_3（\ z），v_3）$具有幽灵类。这意味着它是由Borel子组的共同体产生的。 借助这里开发的技术，我们表明，$ d_2 $频谱序列的$ gl_4（\ z）$的频谱顺序序列是非繁琐的，并且只有当$ gl_3（\ z）$中有一个幽灵类别（请参见11和12）。 $ e_2 $ level的不退化。然后$ d_2 $是非平凡的。因此，我们获得$ h^2（sl_3（\ z），v_3））$是一个幽灵空间，其中$ v_3 $是标准表示。
This paper is a natural continuation of a joint paper with Bajpai, Harder and Moya Giusti \cite{BHHM}, even though it began as an answer to Goncharov's question. It that paper, we had complete description for all representations except for odd symmetric powers and their dual ones. For those representations we were left with two options: certain one dimensional module is a ghost space or not. Here we find the $H^2(SL_3(\Z),V_3)$ has ghost classes. It means that it is generated by a class from the cohomology of the Borel subgroup. With the techniques developed here, we show that the $d_2$ map of the spectral sequence for the boundary cohomology of $GL_4(\Z)$ is non-trivial if and only if there is a ghost class in $GL_3(\Z)$ (see Propositions 11 and 12.) We use a result of Elbaz-Vincent, Gangl and Soule to show that a spectral sequence related to $GL_4(\Z)$ does not degenerate at $E_2$-level. Then $d_2$ is non-trivial. Therefore, we obtain that $H^2(SL_3(\Z),V_3))$ is a ghost space, where $V_3$ is the standard representation.
