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On the Multiplicities of the Primitive Idempotents of a Q-Polynomial Distance-regular Graph

✍ Scribed by Arlene A Pascasio

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 154 KB
Volume: 23
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2002.0607

No coin nor oath required. For personal study only.

✦ Synopsis

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 denote a distance-regular graph with diameter D ≥ 3. Suppose is Q-polynomial with respect to the ordering E 0 , E 1 , . . . , E D of the primitive idempotents. For 0 ≤ i ≤ D, let m i denote the multiplicity of E i . Then

By proving the above theorem we resolve a conjecture of Dennis Stanton.

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