On the Terwilliger algebras of quasi-thin Schurian association schemes

Abstract

An association scheme is triply transitive if its automorphism group is transitive, and the centralizer algebra of a point stabilizer of its automorphism group coincides with the Terwilliger algebra and its subspace $T_0$. In this paper, we give necessary and sufficient conditions for a quasi-thin association scheme to be triply transitive. As a by-product, we give new infinite families of triply-transitive association schemes.