Calculating symmetric group split-standard transformation coefficients using the block selective method: a proof

The split basis for the symmetric group Sn is adapted to Sn and to the product subgroup Sn-axSa. The entries in the matrix that transforms between the split-basis representation and the standard Young-Yamanouchi (YY) basis, the split-standard transformation coefficients, are closely related to a-particle coefficients of fractional parentage. Recently the block selective conjecture was proposed for calculating the coefficients. The conjecture implies that the transformation matrix is directly related to the representation matrix, in the YY basis, of a cycle permutation. We present a proof of this conjecture. (author)