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

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

Let Γ denote a distance-regular graph with diameter D ≥ 3, intersection numbers ai, bi, ci 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 ∈ CAD, where A (resp. AD) is the adjacency matrix (resp. Dth distance matrix) of Γ. If θ = ∞ then M(θ) = CAD. By a pseudo primitive idempotent f...

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ژورنال

عنوان ژورنال: European Journal of Combinatorics

سال: 2004

ISSN: 0195-6698

DOI: 10.1016/s0195-6698(03)00114-8