S. Alisauskas et W. Berej, ON THE PROJECTED BASES FOR SP(4)SUPERSET-OF-U(2) AND THE ORTHOGONALIZATION PROBLEM, Journal of mathematical physics, 35(1), 1994, pp. 344-358
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.