The matrix canonical realizations of the Lie algebra of pseudo-orthogonal group O(m, n) described in the first part of this paper are further investigated. The explicit formulae for values of the Casimir operators (which are multiples of identity in these realizations) are obtained.
We discuss differences between the exact<i>S</i>-matrix for scattering on serial structures and a known factorized expression constructed of single-element<i>S</i>-matrices. As an illustration, we use an exactly solvable model of a quantum wire with two point impurities.
Graph consists of a set of vertices V={Xj: j I}, a set of finite edges L={Ljn:(Xj, Xn) IL I I} and a set of infinite edges L={Lj: Xj IC} attached to them. We regard it as a configuration space of a quantum system with the Hilbert space