Character tables of certain association schemes coming from finite unitary and symplectic groups

Abstract

In this paper we study the character tables of the association schemes obtain from the action of (i) finite unitary groups acting on the set of nonisotropic projective points, and (ii) finite symplectic groups acting on the set of nonisotropic projective lines. It is shown that these character tables are controlled by the character tables of corresponding smaller association schemes which are obtained from the action of the group PGL(2, q) on the cosets by cyclic subgroups Z q + 1 and Z q − 1 , respectively.