The identification of Young tableaux with angular momentum states

Young tableaux are used to label the basis vectors of the standard or Young-Yamanouchi basis of the symmetric group. Despite being used for this purpose for some time, a physical interpretation of what they mean has not been given. Weyl tableaux however, which label the basis vectors of the standard or Gelfand basis of the unitary group, do have a physical interpretation. Weyl tableaux correspond to antisymmetrized states with definite total spin, definite spin projection and definite total angular momentum projection. We discuss how a previously well established link between Young and Weyl tableaux may imply Young tableaux are similarly associated with such states. If such an association could be made, calculations using symmetric group bases could be reduced to simple angular momentum manipulations. In particular this would greatly increase the efficiency of calculating the coefficients of fractional parentage of Sn, which can in turn be used to calculate unitary recoupling coefficients. We present a methodology for determining whether such an association exists. (author)