This paper announces results to be published elsewhere. A triplet (\({\mathfrak g}\), j, \(\omega)\) of a completely solvable Lie algebra \({\mathfrak g}\), a linear operator j of \({\mathfrak g}\), such that \(j^ 2=-1\), and \(\omega\in {\mathfrak g}^*\) is called a normal j-algebra if a few conditions are satisfied. Such a triplet gives rise to a Lie group \(G=N(D)\rtimes G(0)\), where the nilpotent Lie group N(D) is identified with the Shilov boundary of a Siegel domain D of type II. Using the \({\bar \partial}_ b\)- and \(\square_ b\)-operators acting on certain bundles over N(D) a family \(\tilde S_ q\), \(q=0,1,...,n\), of unitary representations of G is defined and their decomposition according to Kirillov-Bernat theory is described. If follows that \(\sum_{0\leq q\leq n}\tilde S_ q\) is multiplicity free.