ON THE PROJECTED BASES FOR SP(4)SUPERSET-OF-U(2) AND THE ORTHOGONALIZATION PROBLEM

The mutual expansion and overlaps of the projected (Smirnov-Tolstoy an d Szpikowski-Berej) bases for the irreducible representations (irreps) of Sp(4) restricted to U(2) are considered. The equivalence relation connecting the overlaps of both (ST and SB) bases after the definite s ubstitution of parameters (up to an elementary factor) is presented. T he overlaps of the Szpikowski-Berej basis states are rearranged to dou ble sums, restricted by the parameters characterizing the multipliciti es of the repeating irreps of subgroup and thus representable in polyn omial forms. The Regge-type symmetry of these new expressions allows t he proof of the earlier conjectured symmetry of the orthogonalization coefficients (OC) for the family of the biorthogonal bases of Sp(4)sup erset of U(2), SU(4)superset of SU(2) XSU(2) and SU(n)superset of SO(n ) for two parametric irreps. The structure of the orthogonalization co efficients for the Szpikowski-Berej basis is also considered. The symm etry of the B-a((abde)(c)) functions (as the conjectured numerator pol ynomials of OC) has been verified by means of computer algebra for som e nontrivial cases.