p-紧群的伴随空间与旗簇
Adjoint spaces and flag varieties of p-compact groups
摘要：
对于具有极大环面$T$的紧李群$G$，Pittie和Smith证明了旗簇$G/T$总是一个稳定的框架边界。我们推广这一类的$p$ -紧群，其中的几何参数被替换为同伦理论的参数表明，类在稳定同伦群的领域所表示的$G/T$是平凡的，甚至$G$ -等变。作为一个应用，我们考虑一个不稳定的$G$ -空间的建设模仿伴随表示领域的$G$的启发工作的第二作者和Kitchloo。这种结构稳定地和$G$ -等变地分裂其顶部单元，然后示出其为$G$的对偶谱。
英文摘要：
For a compact Lie group $G$ with maximal torus $T$, Pittie and Smith showed that the flag variety $G/T$ is always a stably framed boundary. We generalize this to the category of $p$-compact groups, where the geometric argument is replaced by a homotopy theoretic argument showing that the class in the stable homotopy groups of spheres represented by $G/T$ is trivial, even $G$-equivariantly. As an application, we consider an unstable construction of a $G$-space mimicking the adjoint representation sphere of $G$ inspired by work of the second author and Kitchloo. This construction stably and $G$-equivariantly splits off its top cell, which is then shown to be a dualizing spectrum for $G$.
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