Let Phi, Phi' be Leonard systems over a field K, and V, V the vector spaces underlying Phi, Phi', respectively. In this paper, we introduce and discuss a balanced bilinear form on V x 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.
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机译：令Phi，Phi'为场K上的伦纳德系统，而V，V分别为位于Phi，Phi'下的向量空间。在本文中，我们介绍并讨论了V x V'上的平衡双线性形式。这种形式自然是在Q多项式距离正则图的研究中出现的。我们从几个角度描述一个平衡的双线性形式。
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