A CHARACTERIZATION OF THE ASSOCIATION SCHEMES OF HERMITIAN-FORMS

Let Y = (X, {R(i)} o less-than-or-equal-to i less-than-or-equal-to d) be an association scheme whose parameters coincide with those of the association scheme Her(d, q) of Hermitian forms in d-dimensional space over the field GF(q2). Suppose that every edge of the distance-regular graph GAMMA = (X, R1) is contained in a clique of size q. It is shown that if d greater-than-or-equal-to 3 then Y is isomorphic to Her(d, q). In the case d = 2 a generalized quadrangle with the parameters (q, q2) is reconstructed from Y.