The Terwilliger Algebras of Group Association Schemes

The Terwilliger algebra of an association scheme was introduced by Paul Terwilliger [7] in order to study P-and Q-polynomial association schemes. The purpose of this paper is to discuss in detail properties of the Terwilliger algebra of the group association scheme of a finite group. We shall give bounds on the dimension of the Terwilliger algebra, and define triple regularity. Let G be a finite group, C0 = {e}, C1, . . . , Cd the conjugacy classes of G. For i = 0, 1, . . . , d, define