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

Abstract

a b s t r a c tLet 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.

The Terwilliger algebras of the group association schemes of three metacyclic groups

“…In [11], Kim gave a generalization of their result by replacing thin schemes with quasi-thin schemes. The Terwilliger algebra can also be used to study distanceregular graphs (see, e.g., [7,[13][14][15]23]) and distance-biregular graphs (see, [12,16]).…”