A bilinear form relating two Leonard systems

英文摘要：

Let $Φ$, $Φ'$ be Leonard systems over a field $\mathbb{K}$, and $V$, $V'$ the vector spaces underlying $Φ$, $Φ'$, respectively. In this paper, we introduce and discuss a balanced bilinear form on $V\times V'$. 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.