On the Bott suspension map for non-compact Lie groups (Q1890381)

For a classical group \(G\), the Bott suspension map from a symmetric space \(H/K\) into the loop space of another symmetric space \(G/H\) is well known. In this paper the author extends this notion for a non-compact Lie group \(G\). In particular, he studies the two ``extended Bott suspension maps'' \[ \begin{gathered} \text{Gl}(n,\mathbb{C})/O(n, \mathbb{C})\to \Omega(\text{Sp}(n, \mathbb{C})/\text{Gl}(n,\mathbb{C}),\\ \text{Sp}(2n, \mathbb{R})/\text{Gl}(n, \mathbb{R})\to \Omega(\text{Sl}(4n, \mathbb{R})/\text{Sp}(2n, \mathbb{R})).\end{gathered} \]