Hassitt-type young operator expansions I. An orthogonal transformation between ( a ) the Young operators of the symmetric group S A + 1 and ( b ) the two-sided products of the Young operators of S A with the transposition P A , A +

Abstract

An expansion, of the type considered by Hassitt, of the Young operators of S _A+1 in terms of the two-sided products of the Young operators of S _A into the transposition P _{A, A+1} , is derived in complete generality and explicitly evaluated for the symmetry type of the general Wigner nuclear supermultiplet. The expansion allows of a recursive construction of the Young operators which is simpler than that considered, for example, by Thrall. A complete set of Young operators for S ₃ , S ₄ , S ₅ and S ₆ is explicitly constructed and tabulated. In an appendix explicit formulae are given for the most general case.