Deformation of Bott–Samelson varieties and variations of isotropy structures

In the framework of the problem of characterizing complete flag manifolds by their contractions, the complete flags of type F4 and G2 satisfy the property that any possible tower of Bott–Samelson varieties dominating them birationally deforms in a nontrivial moduli. In this paper we illustrate the fact that, at least in some cases, these deformations can be explained in terms of automorphisms of Schubert varieties, providing variations of certain isotropy structures on them. As a corollary, we provide a unified and completely algebraic proof of the characterization of complete flag manifolds in terms of their contractions.