A bilinear form relating two Leonard systems

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10 Citations (Scopus)


Let Φ, Φ be Leonard systems over a field K, and V, V the vector spaces underlying Φ, Φ, respectively. In this paper, we introduce and discuss a balanced bilinear form on V × V. Such a form naturally arises in the study of Q-polynomial distance-regular graphs. We characterize a balanced bilinear form from several points of view.

Original languageEnglish
Pages (from-to)1726-1739
Number of pages14
JournalLinear Algebra and Its Applications
Issue number10
Publication statusPublished - 2009 Oct 15


  • Askey scheme
  • Distance-regular graph
  • Leonard system
  • q-Racah polynomial


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