Groups, buildings, and association schemes

The lecture is supposed to survey some of the lines of development along which an abstract theory of association scheme has been developed so far and along which scheme theory might be developed in the future. I will emphasize mainly on three issues, the incorporation of group theory into scheme theory, the generalization of Sylow's group theoretic theorems to scheme theory, and the incorporation of buildings (in the sense of Jacques Tits) into scheme theory. As for the last issue, I will show that the buildings play exactly the same role in scheme theory that Coxeter groups play in group theory.