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On the representation matrices for the symmetric group adapted to electron‐pair and electron‐group wave functions using graphical methods of spin algebras
Author(s) -
Wilson S.,
Hubač I.
Publication year - 2012
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.24262
Subject(s) - symmetric group , wave function , group (periodic table) , electron , representation (politics) , electron pair , physics , spin (aerodynamics) , representation theory of the symmetric group , basis (linear algebra) , irreducible representation , mathematics , computational chemistry , combinatorics , quantum mechanics , chemistry , geometry , politics , political science , law , thermodynamics
Abstract 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 $S_{n_1 } \times S_{n_2 } \times \ldots \times S_{n_\ell }$ where n 1 + n 2 + … + n ℓ = n . The Serber coupling scheme based on S 2 × S 2 × …× 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. © 2012 Wiley Periodicals, Inc.