Terwilliger algebras of generalized wreath products of association schemes

Abstract

The generalized wreath product of association schemes was introduced by R.~A.~Bailey in European Journal of Combinatorics 27 (2006) 428--435. It is known as a generalization of both wreath and direct products of association schemes. In this paper, we discuss the Terwilliger algebra of the generalized wreath product of commutative association schemes. I will describe its structure and its central primitive idempotents in terms of the parameters of each factors and their central primitive idempotents.Comment: 17 page