The maximal torus normalizer conjecture for connected p-compact groups

Let $X$ be a connected $p$-compact group with maximal torus $T_X$. Its maximal torus normalizer is represented by the loop space $NT_X$. Maximal torus normalizer conjecture. The group $X$ is determined up to equivalence by the loop space $NT_X$. This conjecture extends the Curtis–Wiederhold–Williams theorem from compact connected Lie groups to connected $p$-compact groups. The source gives no resolution in general; the paper proves the corresponding determination result for $Sp(n)$ at $p=2$ when $n\geq 3$.