本学位论文共分为三部分.
      第一部分主要介绍了现阶段有关李群的上同调的计算进展. 有关李群的上同调环的计算问题最早是由Cartan在1929年提出, 后经由拓扑学者的研究对经典李群的上同调有了一定的了解. 2015 年, 段海豹和赵学志通过Schubert计算的方法给出了5种例外李群的整系数上同调, 后在2016年给出了一般紧李群的上同调的计算方法, 并在文章中给出了一些伴随李群的上同调计算结果. 然而, 有关经典李群的上同调的计算问题仍未完全解决. 我的主要工作是计算了SU(n)/Zq的上同调, 其中Zq为SU(n)的中心Zn的子群, 我在第一部分最后列出了我的计算结果.
      第二部分主要是为了计算上同调所需要用到的预备知识, 主要有旗流型的相关性质, 对纤维化T→G→G/T的谱序列的分析和性质, 一些Steenrod代数的相关知识, Schubert计算的主要结论和二项式系数的两条性质. 第二部分主要是为了具体计算服务.
      第三部分为我的主要工作, 给出了SU(n)/Zq的上同调的具体计算过程. 首先从纤维化T→SU(n)→SU(n)/T的谱序列进行分析, 得到E**项的计算结果. 后将E**项中的生成元通过商映射映到H*中, 再根据Steenrod代数的相关性质确定生成元之间满足的关系, 由此得到模p系数的上同调结果. 我们根据整系数同调环可分解为自由部分和挠部分的直和, 分别计算自由部分和挠部分, 即可得到整系数上同调.

This thesis consists of three parts.
In the first part, we introduce the development of the calculation of the cohomologies of Lie groups far away. The problem of computing the cohomologies of Lie groups was raised by Cartan in 1929. After that, topologyist, like Mimura, Toda, Chevalley, etc. knowed more and more about the cohomologies of Lie groups. In 2015, H. Duan and X. Zhao finished the integral cohomologies of 5 exceptional Lie groups. In 2016, H. Duan gave a normal way to calculate the cohomology of a compact Lie group, and listed the cohomologies of some adjointed Lie groups in the paper. However, there are also many other problem about the cohomolgy of classical Lie group, so I calculate the cohomolgy of SU(n)/Zq, where Zq is the subgroup of Zn, the center of SU(n).I list the result of my work in the last of the first part.
In the second part, we introduce the preparatory knowledge we will used in the third part. It included the knowledge of flag manifoldm, the analysis and properties of the spectral sequence of the fibration T→G→G/T, properties of Steenrod algebra, the main result of Schubert calculation and some proposition of binomial coefficient.
In the third part, we give the main process of calculating the cohomology of SU(n)/Zq. Firstly, we begin with the spectral sequence of the fibration T→SU(n)→SU(n)/T. Then, we get the result of E**-term. We can map the generators of E**-term to H*. Next, by the properties of Steenrod algebra, we get the mod-p cohomology ring. According to the proposition that the integral cohomolgy can be decomposed as the direct sum of the free part and p-primary component, so we calculate the two part separately. Finally, we get the integral cohomology of SU(n)/Zq.