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Direct evaluation of spin representation matrices and ordering of permutation‐group elements
Author(s) -
Rettrup Sten
Publication year - 1986
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.560290111
Subject(s) - permutation (music) , eigenfunction , representation (politics) , permutation matrix , symmetric group , group (periodic table) , mathematics , computation , spin (aerodynamics) , permutation group , matrix (chemical analysis) , matrix representation , quadratic equation , pure mathematics , combinatorics , algebra over a field , eigenvalues and eigenvectors , physics , algorithm , quantum mechanics , chemistry , geometry , politics , political science , acoustics , law , thermodynamics , chromatography
A direct and general method is presented for constructing the orthogonal spin representation matrices (irreps) of the permutation group corresponding to the Yammanouchi‐Kotani coupling scheme. For arbitrary permutations the irreps are constructed directly from the Young tableaus by a process which is, in general, only quadratic in the number of spin eigenfunctions, but which in actual computations becomes linear on vector computers for moderate sizes of the matrices. We also introduce a graphical representation of the group elements and a universal lexical ordering of permutations. The methods have been implemented and computational examples are presented.