Permutational symmetry of many particle states

The symmetry of the Nth rank tensor basis for an irreducible representation of U (n) under the operations of the permutation group has been investigated. It has been found that symmetrized linear combinations of the elements of the matrix algebra of S N lead to a tensor basis for U (n) yielding the same matrix elements as the Gel’fand–Tsetlin basis for the generators E i,i±1 of U (n). Based on these developments an algorithm has been developed for directly determining the matrix elements of the generators E i j (j≠i±1) of U (n) using a pattern calculus.