English

A bilinear form relating two Leonard systems

Rings and Algebras 2010-05-21 v2

Abstract

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

Cite

@article{arxiv.0807.0385,
  title  = {A bilinear form relating two Leonard systems},
  author = {Hajime Tanaka},
  journal= {arXiv preprint arXiv:0807.0385},
  year   = {2010}
}

Comments

15 pages

R2 v1 2026-06-21T10:56:51.500Z