The one-particle fractional parentage coefficients for totally antisymmetric states of n identical fermions have been calculated by diagonalizing the Casimir operators of the unitary and symplectic groups. They are tabulated for n up to the half-filled shell for j ≦ 11 2, and n ≦ 5 for j = 13 2 and 15 2 respectively. The coefficients for totally symmetric states of identical bosons, dn (n ≦ 7), fn(n ≦ 6) and gn(n ≦ 5) were determined in a similar manner.
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t This work was supported by the U.S. Atomic Energy Commission and the Higgins Scientific Trust Fund. This report made use of the Princeton computer facilities supported in part by National Science Foundation Grant NSF-GP579.