Spectra of Bipartite P- and Q-Polynomial Association Schemes

Abstract

Let Y=(X,{R i }0≤i≤D) denote a symmetric association scheme with D≥3, and assume Y is not an ordinary cycle. Suppose Y is bipartite P-polynomial with respect to the given ordering A0, A1,…, A D of the associate matrices, and Q-polynomial with respect to the ordering E0, E1,…,E D of the primitive idempotents. Then the eigenvalues and dual eigenvalues satisfy exactly one of (i)–(iv).