Levi flat hypersurfaces are characterized by vanishing of the Levi form on them. Their regular part is foliated by complex hypersurfaces, this is called the Levi foliation. It is an open question whether one can extend this foliation to the ambient space. As example of Brunella shows, near singular points the extension may exist in general only as a singular holomorphic web. A smooth holomorphic web is simply the union of several foliations. A singular web is a more general object which loosely can be thought of as a foliation with branching. In this talk I will give a detailed background concerning holomorphic webs, and will discuss some recent progress on extension of the Levi foliation. This is joint work with A. Sukhov.

We review basic results of the representation theory of compact connected Lie groups.