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

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

2003-06-08

arxiv.org/abs/math/0306142v1

Mathematics

Combinatorics

14 pages

Scientific paper

Let $\Gamma$ 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 $\Gamma$ and the split
decomposition for $\Gamma$. We describe how these decompositions are related.

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