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The Terwilliger algebra of a distance-regular graph of negative type

✍ Scribed by Štefko Miklavič

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
258 KB
Volume
430
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let denote a distance-regular graph with diameter D 3. Assume has classical parameters (D, b, α, β) with b < -1. Let X denote the vertex set of and let A ∈ Mat X (C) denote the adjacency matrix of . Fix x ∈ X and let A * ∈ Mat X (C) denote the corresponding dual adjacency matrix. Let T denote the subalgebra of Mat X (C) generated by A, A * . We call T the Terwilliger algebra of with respect to x. We show that up to isomorphism there exist exactly two irreducible T-modules with endpoint 1; their dimensions are D and 2D -2. For these T-modules we display a basis consisting of eigenvectors for A * , and for each basis we give the action of A.

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