Maximal dimension of groups of symmetries of homogeneous 2-nondegenerate CR structures of hypersurface type with a 1-dimensional Levi kernel

Abstract

We prove that for every $n\ge 3$ the sharp upper bound for the dimension of the symmetry groups of homogeneous, 2-nondegenerate, $(2n+1)$-dimensional CR manifolds of hypersurface type with a $1$-dimensional Levi kernel is equal to $n^2+7$, and simultaneously establish the same result for a more general class of structures characterized by weakening the homogeneity condition. This supports Beloshapka's conjecture stating that hypersurface models with a maximal finite dimensional group of symmetries for a given dimension of the underlying manifold are Levi nondegenerate.

38 pages, the main revision is that the paper now directly states all results for the more general setting of structures admitting constant reduced modified symbols, rather than just for homogeneous structures