Steinness of the Basic $\mathrm{GL}_n$ Local Shimura Tower in Odd Rank

We prove Steinness over $\breve{\mathbf{Q}}_p$ for the basic local Shimura tower attached to $G=\mathrm{GL}_n$, $μ=(1,1,0^{n-2})$, with basic Newton slope $2/n$, for every odd $n\ge3$, at every finite level and for every prime $p$. The proof proceeds by constructing global analytic functions from th