The Terwilliger algebra of the Johnson scheme J(N, D) revisited from the viewpoint of group representations

Let T = T(x(0)) be the Terwilliger algebra of the Johnson scheme J(N, D), where x(0) is a fixed base point. In Liang et al. (2017), an observation is made on the parameters of Leonard systems that arise from the irreducible representations of T. This paper accounts for the observation from the viewpoint of group representations. In particular, it is shown that T is isomorphic to the centralizer algebra for the stabilizer of the base point x(0) in the automorphism group of J(N, D). (C) 2018 Elsevier Ltd. All rights reserved.