Group of canonical transformations and the method of $K$ harmonics

The method of the group of canonical transformations $Sp (2, R)$ (or $SU (1,1)$) is used for constructing the $K$-harmonics with given permutational symmetry and evaluating the energy matrix. The parentage technique for constructing the $K$-harmonics is developed which is similar to the translation-invariant shell model, but includes the noncompact $nj$-symbols for the group $SU (1,1)$ and the Raynal–Rewai coefficients.