Birationally equivalent Landau-Ginzburg models on cotangent bundles and adjoint orbits

We show that the Lie potential on the minimal semisimple adjoint orbit ${\mathcal{O}}_n$ of $\mathfrak{s}\mathfrak{l}(n+1,\mathbb{C})$ coincides with toric potential on $T^{\ast }{\mathbb{P}}^n$. We then study the corresponding Landau-Ginzburg models in deformation families and give some examples of how the deformations affect the mirrors.