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The displacement and split decompositions for a $Q$-polynomial distance-regular graph

Paul Terwilliger
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Abstract

Let $Γ$ denote a $Q$-polynomial distance-regular graph with diameter at least three and standard module $V$. We introduce two direct sum decompositions of $V$. We call these the displacement decomposition for $Γ$ and the split decomposition for $Γ$. We describe how these decompositions are related.

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Paul Terwilliger. 2003-06-08. The displacement and split decompositions for a $Q$-polynomial distance-regular graph. https://arxiv.org/abs/math/0306142

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