20.500.12556/RUP-172
The Terwilliger algebra of a distance-regular graph of negative type
Let ▫$\Gamma$▫ denote a distance-regular graph with diameter ▫$D \ge 3$▫. Assume ▫$\Gamma$▫ has classical parameters ▫$(D,b,\alpha,\beta)▫$ with ▫$b < -1$▫. 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 $A^\ast \in {\mathrm{Mat}}_X(\mathbb{C})$ denote the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ${\mathrm{Mat}}_X(\mathbb{C})$ generated by ▫$A,A^\ast$▫. We call ▫$T$▫ the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. We show that up to isomorphism there exist exactly two irreducible ▫$T$▫-modules with endpoint 1; their dimensions are ▫$D$▫ and ▫$2D-2$▫. For these ▫$T$▫-modules we display a basis consisting of eigenvectors for ▫$A^\ast$▫, and for each basis we give the action of ▫$A$▫.
distance-regular graph
negative type
Terwilliger algebra
true
true
false
Angleški jezik
Angleški jezik
Delo ni kategorizirano
2013-10-15 12:04:34
2013-10-15 12:04:34
2024-03-01 11:54:44
0000-00-00 00:00:00
2009
0
0
str. 251-270
no. 1
Vol. 430
2009
0000-00-00
NiDoloceno
NiDoloceno
NiDoloceno
0000-00-00
0000-00-00
0000-00-00
0024-3795
519.1
2132965
http://dx.doi.org/10.1016/j.laa.2008.07.013
1
https://repozitorij.upr.si/Dokument.php?lang=slv&id=172
Inštitut Andrej Marušič
0
0
0