The displacement and split decompositions for a $Q$-polynomial distance-regular graph
arXiv:math/0306142
Abstract
Let $Î$ 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 $Î$ and the split decomposition for $Î$. We describe how these decompositions are related.
14 pages