A bilinear form relating two Leonard systems

Abstract

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

15 pages

References in corpus (1)

• Some algebra related to $P$-and $Q$-polynomial association schemes

Cited by in corpus (7)

• Distance-regular graphs
• Commutative association schemes
• Dual Polar Graphs, a nil-DAHA of Rank One, and Non-Symmetric Dual q-Krawtchouk Polynomials
• A classification of sharp tridiagonal pairs
• On the shape of a tridiagonal pair
• Vertex subsets with minimal width and dual width in $Q$-polynomial distance-regular graphs
• The Erdős-Ko-Rado basis for a Leonard system