TITLE:
Imprimitive Q-polynomial Association Schemes
ABSTARACT:
It is well known that imprimitive P-polynomial association schemes X
= (X,{Ri}i = 0,...,d) with k1 > 2 are
either bipartite or antipodal, i.e., intersection numbers satisfy either
ai = 0 for all i, or bi = cd-i for all i not equal to [d/2].
In this paper, we show that imprimitive Q-polynomial association schemes
X = (X,{Ri}i = 0,...,d) with d>6 and k*1 >2 are
either dual bipartite or dual antipodal,
i.e., dual intersection numbers satisfy either
a*i = 0 for all i, or b*i = c*d-i for all i not equal to [d/2].
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