A GRAPHICAL APPROACH TO PERMUTATION GROUP REPRESENTATIONS FOR MANY-ELECTRON SYSTEMS

摘要

A simple procedure is presented for obtaining the standard Young tableaux for the representation [(N/2) + S,(N/2) - S] of the permutation group F-N 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. (C) 1996 John Wiley & Sons, Inc. [References: 4]