On non-displaceable Lagrangian submanifolds in two-step flag varieties

Abstract

We prove that the two-step flag variety $\mathcal{F}\ell (1,n;n+1)$ carries a non-displaceable and non-monotone Lagrangian Gelfand--Zeitlin fiber diffeomorphic to $S^3\times T^{2n-4}$ and a continuum family of non-displaceable Lagrangian Gelfand--Zeitlin torus fibers when $n>2$.

21 pages, 4 figures