On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph
College
College of Science
Department/Unit
Mathematics and Statistics Department
Document Type
Article
Source Title
European Journal of Combinatorics
Volume
23
Issue
8
First Page
1073
Last Page
1078
Publication Date
1-1-2002
Abstract
Ito, Tanabe and Terwilliger recently introduced the notion of a tridiagonal pair. We apply their results to distance-regular graphs and obtain the following theorem. THEOREM. Let Γ denote a distance-regular graph with diameter D ≥ 3. Suppose Γ is Q-polynomial with respect to the ordering E0, E1,..., ED of the primitive idempotents. For 0 ≤ i ≤ D, let mi, denote the multiplicity of E i. Then (i) mi-1 ≤ mi (1 ≤ i ≤ D/2), (ii) mi ≤ mD-i (0 ≤ i ≤ D/2). By proving the above theorem we resolve a conjecture of Dennis Stanton. © 2002 Elsevier Science Ltd. All rights reserved.
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Digitial Object Identifier (DOI)
10.1006/eujc.2002.0607
Recommended Citation
Pascasio, A. A. (2002). On the multiplicities of the primitive idempotents of a Q-polynomial distance-regular graph. European Journal of Combinatorics, 23 (8), 1073-1078. https://doi.org/10.1006/eujc.2002.0607
Disciplines
Algebra
Keywords
Algebras, Linear; Polynomials
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