Terwilliger algebras of generalized wreath products of association schemes

Abstract

The generalized wreath product of symmetric association schemes was introduced by R.A.Bailey in the European Journal of Combinatorics 27 (2006) 428-435. It is recognized as a unification of both the wreath product and the direct product of symmetric association schemes. While its potential applicability to any association scheme had been implied, this paper provides a formal and explicit confirmation of that claim. Moreover, we establish the irreducible representations of its adjacency algebra and Terwilliger algebra.