Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra

الأصل · EN

Let Γ denote a distance-regular graph with diameter D≥ 3 and Bose-Mesner algebra M. For θ∈ C∪ ∞ we define a 1 dimensional subspace of M which we call M(θ). If θ∈ C then M(θ) consists of those Y in M such that (A-θI)Y∈ C AD, where A (resp. AD) is the adjacency matrix (resp. Dth distance matrix) of Γ. If θ= ∞ then M(θ)= C AD. By a pseudo primitive idempotent for θ we mean a nonzero element of M(θ). We use pseudo primitive idempotents to describe the irreducible modules for the Terwilliger algebra, that are thin with endpoint one.