Kac-Moody群及其旗流形的庞加莱级数和有理上同调环
Poincaré series and rational cohomology rings of Kac-Moody groups and their flag manifolds
摘要：
本文研究了不定Kac-Moody群的有理上同调环及其旗流形。通过从Poincaré级数中提取上同调的信息，我们可以确定Kac-Moody群的有理上同调环及其旗流形.由于Kac-Moody群及其旗流形是有理形式的，我们还确定了它们的有理同伦群和有理同伦类型.
英文摘要：
In this paper, we study the rational cohomology rings of indefinite Kac-Moody groups and their flag manifolds. By extracting the information of cohomology from the Poincaré series, we are able to determine the rational cohomology rings of Kac-Moody groups and their flag manifolds. Since Kac-Moody groups and their flag manifolds are rational formal, we also determine their rational homotopy groups and rational homotopy types.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
