A graphical approach to permutation group representations for many-electron systems

✍ Scribed by C. R. Sarma; M. A. H. Ahsan; Sten Rettrup

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 422 KB
• Volume: 58
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1996)58:6<637::aid-qua6>3.0.co;2-z

✦ Synopsis

A simple procedure is presented for obtaining the standard Young tableaux for the representation [( N/2) + S, (N/2) -S ] of the permutation group -U-., for an N-electron system in spin state S directly from the spin branching diagram. We redefine the coordinate axes of the branching diagram to obtain a graph in terms of the partitions of the two-rowed Young diagram and define walks in this graph which yield directly the first rows of the allowed standard Young tableaux spanning a given representation when suitable weights have been assigned to the nodes in the graph. The allowed states are in a lexically ordered form and permit going easily from an index to an array and vice versa. 0 1996 John Wiley & Sons, Inc. of the permutation group PN. It represents basically a diagrammatic description of the canonical subgroup restriction T electron systems [1-31 provides a useful route and yields the various two-rowed Young diagram cursively starting with PI. It also provides a basis spanning the representations " I " given representation. labeled boxes 1, i = Starting from P i , we add 1,. .