Transformation between the Young - Yamanouchi basis and its dual

Motivated by the aim of finding generalized transformation coefficients for the symmetric group, we calculate the matrix which transforms the basis functions of the Young - Yamanouchi basis into the basis functions of its dual. Our approach is to derive the representation matrices for both bases and then determine the transformation matrix. The dual basis is associated with the subgroup chain , whereas the usual YY basis is associated with the subgroup chain . A combinatorial technique, jeu de taquin , is used to define the basis, via the Young - Yamanouchi symbols and Young tableaux with which the basis functions can be indexed.