The Terwilliger algebra of the incidence graphs of Johnson geometry, II

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