Generalized back coupling rules for the Racah algebra of Gln
John J. Sullivan · Journal of Mathematical Physics · 1980
Two subgroup relations for double coset matrix elements (DCME) of the symmetric group SN are derived by considering the processes of subduction and induction. The duality of outer product coupling in SN and inner product coupling in Gln identifies these as generalized back coupling rules for the Racah algebra of Gln. An iterative procedure for evaluating the DCME, once a consistent phase convention is established, is given. As an example the Racah sum formula for the Clebsch–Gordan coefficients of SU2 is derived from consideration of SN coupling only.