On The Representation Matrices For The Symmetric Group Adapted To Electron-Pair And Electron-Group Wave Functions Using Graphical Methods Of Spin Algebras

Using 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-n1 x S-n2 x ... x S-nt where n(1) + n(2) + ... + n(t) = n. The Serber coupling scheme based on S-2 x S-2 x ... x S-2 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. (c) 2012 Wiley Periodicals, Inc.