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Title:The Terwilliger algebra of a distance-regular graph of negative type
Authors:Miklavič, Štefko (Author)
Files:URL http://dx.doi.org/10.1016/j.laa.2008.07.013
 
Language:English
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract: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 ▫$A$▫.
Keywords:distance-regular graph, negative type, Terwilliger algebra
Year of publishing:2009
Number of pages:str. 251-270
Numbering:Vol. 430, no. 1
ISSN:0024-3795
UDC:519.1
COBISS_ID:2132965 Link is opened in a new window
Views:1674
Downloads:76
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