On automorphisms of CR-submanifolds of complex Hilbert space

It is shown that there exists only one tolally nondegenerate CR manifold of type $(n,\infty)$ (up to the formal equivalence), and the dimension of its Lie algebra $\mathfrak{g}_{+}$ of positively graded formal tangent vector fields is infinite. Examples of manifolds of type $(n,\infty)$ with algebras of any given in advance finite dimension are presented.