Abstract
Let J(n,m,m+1) denote the incidence graph of Johnson geometry. It is well known that the Johnson graph J(n,m) is a halved graph of J(n,m,m+1). Let T and T′ be the Terwilliger algebra of J(n,m,m+1) and J(n,m), respectively. In this paper, we focus on the structures of irreducible T-modules, and then completely determine T. Furthermore, we discover the relationship between irreducible modules of T and T′. As a result, the algebra T′ is determined again.
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