CHARACTER TABLES OF THE ASSOCIATION SCHEMES OF FINITE ORTHOGONAL GROUPS ACTING ON THE NONISOTROPIC POINTS

We study the character tables of the association schemes obtained from the following actions of finite (simple) orthogonal groups: 1. (i) O2m+(2n) and O2m-(2n) acting on the set of nonisotropic points. 2. (ii) O2m+(pn) and O2m-(pn) (p an odd prime) acting on each half of the set of nonisotropic points. 3. (iii) O2m + 1(pn) (p an odd prime) acting on the set of square-type and the set of non-square-type nonisotropic points. It is shown that the character tables of the association schemes in the above (i) and (ii) are controlled by the character table of the group PSL(2, q), while that the character tables of the association schemes in (iii) are controlled by the character tables of the association schemes obtained from the action of the group PGL(2, q) acting on the cosets by dihedral subgroups D2(q - 1) and D2(q + 1), respectively. © 1990.