The symmetric group: Algebraic formulas for some S f 6j symbols and S f⊇S f1×S f2 3j m symbols
R. W. Haase, Rainer Dirl · Journal of Mathematical Physics · 1986
Explicit rank-dependent expressions have been obtained for some symmetric group (Sf) 6j symbols and some Sf⊇Sf1×Sf2 3jm symbols using Butler’s recursion method. A key point in deriving these results is the use of the reduced notation introduced by Murnaghan to label irreps. Various symmetries of the 6j and 3jm symbols have been imposed. These include the complex conjugation, permutation, and transpose conjugation. We incorporate a new symmetry that arises from the occurrence of the two isomorphic direct product groups Sf1×Sf2 and Sf2×Sf1 as subgroups of Sf. In relation to the tables of 6j and 3jm symbols presented, a discussion is given of the symmetric group-unitary group duality.