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Tight Distance-regular Graphs and the Subconstituent Algebra

2002
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European journal of combinatorics (Print)
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We consider a distance-regular graph with diameter D ≥ 3, intersection numbers a i , b i , c i and eigenvalues k = θ 0 > θ 1 > · · · > θ D . Let X denote the vertex set of and f x x ∈ X. where A denotes the adjacency matrix of and E * i denotes the projection onto the ith subconstituent of with respect to x. T is called the subconstituent algebra (or Terwilliger algebra) of with respect to x. An irreducible T -module W is said to be thin whenever dim where E i denotes the primitive idempotent

doi:10.1006/eujc.2002.0597
fatcat:ocquedjr2jdobomyhvidoln3le