Ulrich Schur bundles on flag varieties

In this paper, we study equivariant vector bundles on partial flag varieties arising from Schur functors. We show that a partial flag variety with three or more steps does not admit an Ulrich bundle of this form with respect to the minimal ample class. We classify Ulrich bundles of this form on two-step flag varieties F(1,n-1;n), F(2,n-1;n), F(2,n-2;n), F(k,k+1;n) and F(k,k+2;n). We give a conjectural description of the two-step flag varieties which admit such Ulrich bundles.