On the Construction of Orthogonal Matrix Basis Elements of Finite Group Algebras Symmetry Adapted to a Subgroup
John J. Sullivan · Journal of Mathematical Physics · 1971
The matrix basis elements of a finite group g(Γ, mn) are put in a form |Γm〉 〈Γn| suggestive of a dyadic in operator space. It is shown that if a subgroup H exists for which Γ ↓ H = Σγi, then these operators may be symmetry adapted to the subgroup via |Γγjm〉 Qj†ba. Necessary and sufficient conditions for constructing the elements Qj†, b and a are given. Particular application of the procedure to the bipartition representations of the symmetric group is made.