The Block Selective Conjecture For Calculating A Class Of Symmetric Group Transformation Coefficients

The split-basis for the symmetric group S-n is adapted to S-n and to the product subgroup S-a x S-b, where a + b = n We are interested in the matrices transforming between these split-bases and the standard Young-Yamanouchi basis. We discuss some general problems with the various techniques available for calculating those matrices. Some of those problems are overcome by our block selective conjecture. This conjecture directly relates the transformation matrix to a representation matrix, in the Young-Yamanouchi basis, of a cycle permutation.