The Dunkl-Watanabe duality, II

Last year, I gave a talk at SUSTECH with the same title, in which I made two conjectures. This is a continuation of the talk. It turns out that one of them is correct and the other is wrong. I will discuss the coherent configuration that arises from the action of a maximal parabolic subgroup H of GL(N,q) acting on the set of all subspaces ̃X of F_q^N. The 1st and 2nd eigenmatrices of the association scheme on each fibre are explictly given in terms of those of q-Johnson schemes and bilinear forms schemes. I will explain the structure of the Bose-Mesner algebra of the association scheme in terms of group characters, and how it is globally connected to others in the coherent configuration. This is joint work with Xiaoye Liang.