The Terwilliger algebras of Johnson graphs

Let J(n, m) denote the Johnson graph with vertex set X. Fix a vertex x epsilon X. Let T = T(x) denote the Terwilliger algebra of J(n, m) corresponding to x. In this paper we study the structure of T under the assumption that m >= 3 and n >= 4m. Let U(sl2) be the universal enveloping algebra of sl(2). We display a C-algebra homomorphism v : U(sl(2)) -> T. We show that T is generated by the image of v and some central elements of T. We obtain these results using the theory of Leonard pairs. (C) 2013 Elsevier Inc. All rights reserved.