Association schemes coming from minimal flats in classical polar spaces

Let denote a 2ν-dimensional vector space over a finite field Fq with a non-degenerate form of Witt index ν, and G denote the corresponding isometry group. Let W be a fixed maximal flat, and Θ be the set of all the minimal flats not contained in W. The set-wise stabilizer of W in G acts transitively on Θ and thus this action determines an association scheme. In this paper, we compute the intersection numbers and character tables for these schemes.