The Terwilliger Algebra of a Distance-Regular Graph of Negative Type

Understand

Let $\Gamma$ denote a distance-regular graph with diameter $D \ge 3$.

• Assume $\Gamma$ has classical parameters $(D,b,\alpha,\beta)$ with $b < -1$.
• Let $X$ denote the vertex set of $\Gamma$ and let $A \in MX$ denote the adjacency matrix of $\Gamma$.
• Fix $x \in X$ and let $A^* \in MX$ denote the corresponding dual adjacency matrix.