Formal self-duality and numerical self-duality for symmetric association schemes

Kazumasa Nomura, Paul Terwilliger

Let $\mathcal{X}=(X,\{R_i{\}}_{i=0}^d)$ denote a symmetric association scheme. Fix an ordering $\{E_i{\}}_{i=0}^d$ of the primitive idempotents of $\mathcal{X}$, and let $P$ (resp.…