Varietal Terwilliger algebras arising from wreath products of rank two association schemes

As abstractions of Terwilliger algebras, generalized Terwilliger algebras and varietal Terwilliger algebras have been studied in [5,6,17]. In general, it is difficult to determine the structure of a varietal Terwilliger algebra. As proposed in the concluding remarks in [4], in this paper we study the structures of those varietal Terwilliger algebras arising from the wreath products of rank two association schemes. In particular, we give the explicit formulas for their central primitive idempotents. Applications to Terwilliger algebras of association schemes are also discussed, and an affirmative answer to the Terwilliger conjecture mention in [4] is given. (C) 2018 Elsevier Inc. All rights reserved.