On the representation matrices for the symmetric group adapted to electron‐pair and electron‐group wave functions using graphical methods of spin algebras

Abstract

AbstractUsing graphical methods of spin algebras, we present a direct method for the determination of the representation matrices of the symmetric group in a basis adapted to electron‐pair and electron‐group wave functions. In particular, we consider nonstandard representations adapted to $S_{n_1 } \times S_{n_2 } \times \ldots \times S_{n_\ell }$ where n1 + n2 + … + nℓ = n. The Serber coupling scheme based on S2 × S2 × …× S2 is a special case suited for electron‐pair wave functions. Our approach exploiting graphical methods of spin algebras is contrasted with the use of Young diagrams and tableaux, Yamanouchi symbols and branching diagrams. © 2012 Wiley Periodicals, Inc.