Q-polynomial distance-regular graphs with a [sub] 1 [equal] 0 and a [sub] 2 [not equal] 0

Povzetek

Let ▫$\Gamma$▫ denote a ▫$Q$▫-polynomial distance-regular graph with diameter ▫$D \ge 3$▫ and intersection numbers ▫$a_1=0$▫, ▫$a_2 \ne 0$▫. Let ▫$X$▫ denote the vertex set of ▫$\Gamma$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫$\Gamma$▫. Fix ▫$x \in X$▫ and let denote $A^\ast \in {\mathrm{Mat}}_X ({\mathbb{C}})$ the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫$A{\mathrm{Mat}}_X ({\mathbb{C}})$▫ generated by ▫$A$▫, ▫$A^\ast$▫. We call ▫$T$▫ the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. We show that up to isomorphism there exists a unique irreducible ▫$T$▫-module ▫$W$▫ with endpoint 1. We show that ▫$W$▫ has dimension ▫$2D-2$▫. We display a basis for ▫$W$▫ which consists of eigenvectors for ▫$A^\ast$▫. We display the action of ▫$A$▫ on this basis. We show that ▫$W$▫ appears in the standard module of ▫$\Gamma$▫ with multiplicity ▫$k-1$▫, where ▫$k$▫ is the valency of ▫$\Gamma$▫.

Ključne besede

matematika;teorija grafov;razdaljno regularni grafi;matrika sosednosti;Terwilligerjeva algebra;mathematics;graph theory;adjacency matrix;distance-regular graph;Terwilliger algebra;

Podatki

Jezik:	Angleški jezik
Leto izida:	2008
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UP - Univerza na Primorskem
UDK:	519.17
COBISS:	14627929
ISSN:	0195-6698
Št. ogledov:	4075
Št. prenosov:	30
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarne ključne besede:	matematika;teorija grafov;razdaljno regularni grafi;matrika sosednosti;Terwilligerjeva algebra;
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 192-207
Letnik:	ǂVol. ǂ30
Zvezek:	ǂno. ǂ1
Čas izdaje:	2009
DOI:	10.1016/j.ejc.2008.02.001
ID:	1473516