A simple class of U ( N ) Racah coefficients and their application

Abstract

Using permutation group techniques, a general expression is derived for the special class of U ( N ) Racah coefficients for which the representations [ f 1 ] and [ f 3 ] in the recoupling matrix for [ f 1 ]×[ f 2 ]×[ f 3 ]→[ f ] are either both totally antisymmetric or both totally symmetric. For the totally antisymmetric case further specialization gives a simple expression for a U ( N ) Racah coefficient which is needed in taking the average of the product of operators over the states of an irreducible representation of U ( N ), where this result can be useful in the study of identical fermion systems by spectral distribution methods.