arXiv subjects
Publications and source records attributed to M. Nacinovich.
We study the correspondence between equivalence classes of pairs consisting of real semisimple Lie algebras and their Cartan subalgebras and involutions of the corresponding root system. This can be graphically described by introducing \emph{$S\!${-} and $Σ$-diagrams}, generalizing those of Satake and Vogan.
Let M be a smooth locally embeddable CR manifold, having some CR dimension m and some CR codimension d. We find an improved local geometric condition on M which guarantees, at a point p on M, that germs of CR distributions are smooth functions, and have extensions to germs of holomorphic functions on a full ambient neighborhood of p. Our condition is a form of weak pseudoconcavity, closely related to essential pseudoconcavity as introduced in [HN1]. Applications are made to CR meromorphic functions and mappings. Explicit examples are given which satisfy our new condition,but which are not pseudoconcave in the strong sense. These results demonstrate that for codimension d > 1, there are additional phenomena which are invisible when d = 1.