A duality between pairs of split decompositions for a $Q$-polynomial distance-regular graph
| dc.creator | Kim, Joohyung | |
| dc.date | 2007-05-01 | |
| dc.date.accessioned | 2026-07-07T07:59:03Z | |
| dc.date.available | 2026-07-07T07:59:03Z | |
| dc.description | Let $Γ$ denote a $Q$-polynomial distance-regular graph with diameter $D \geq 3$ and standard module $V$. Recently Ito and Terwilliger introduced four direct sum decompositions of $V$; we call these the $(μ,ν)$--{\it split decompositions} of $V$, where $μ, ν\in \lbrace \downarrow, \uparrow \rbrace$. In this paper we show that the ($\downarrow,\downarrow$)--split decomposition and the ($\uparrow,\uparrow$)--split decomposition are dual with respect to the standard Hermitian form on $V$. We also show that the ($\downarrow,\uparrow$)--split decomposition and the ($\uparrow,\downarrow$)--split decomposition are dual with respect to the standard Hermitian form on $V$. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0705.0167 | |
| dc.identifier | http://arxiv.org/abs/0705.0167 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128225 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E30 | |
| dc.title | A duality between pairs of split decompositions for a $Q$-polynomial distance-regular graph | |
| dc.type | text |