Tables of the SU(mn) [conditional] SU(m) X SU(n) : coefficients of fractional parentage

The aim of this book is to give a unified presentation of the local stereological methods developed within the last ten years. "Local Stereology" is a collection of local integral geometric formulae which can be used in the non-parametric estimation of local spatial characteristics. The main applications are in particle analysis and in the study of the spatial arrangement of structures. Only very weak assumptions are needed for the structures under study. For instance, specific particle shape assumptions are not necessary The f2-particle coefficients of fractional parentage for the group chain SU(mn) ⊃ SU(m) x SU(n) or U(mn) ⊃ U(m) x U(n), with arbitrary m and n and with as many as possible symmetries, are tabulated for systems with up to six particles and for f2 equal up to three. All the coefficients are in the form of square roots of simple fractions. The algorithm for the CPF as well as the symmetries of the CFP are discussed. The f 2 -particle coefficients of fractional parentage for the group chain SU(mn)? SU(m) x SU(n) or U(mn)? U(m) x U(n), with arbitrary m and n and with as many as possible symmetries, are tabulated for systems with up to six particles and for f 2 equal up to three. All the coefficients are in the form of square roots of simple fractions. The algorithm for the CPF as well as the symmetries of the CFP are discussed