On rigidity of universal model surfaces

There is a class of models of non–degenerate CR submanifolds satisfying certain universality conditions introduced by Beloshapka. The following rigidity of CR automorphisms was conjectured for this class of universal model surfaces: All CR automorphisms in the stabilizer of a point are linearizable. I will prove this conjecture in two steps. Firstly, I identify these universal model surfaces with standard real submanifolds related to universal/free Levi–Tanaka algebras. Then I prove the equivalent claim to the conjecture stating that these Levi–Tanaka algebras have trivial Tanaka prolongation.