The Terwilliger algebra of a distance-regular graph of negative type

Miklavič, Štefko

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Title:	The Terwilliger algebra of a distance-regular graph of negative type
Authors:	ID Miklavič, Štefko (Author)
Files:	http://dx.doi.org/10.1016/j.laa.2008.07.013
Language:	English
Work type:	Not categorized
Typology:	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
PID:	20.500.12556/RUP-172
ISSN:	0024-3795
UDC:	519.1
COBISS.SI-ID:	2132965
Publication date in RUP:	15.10.2013
Views:	4012
Downloads:	112
Metadata:
:	MIKLAVIČ, Štefko, 2009, The Terwilliger algebra of a distance-regular graph of negative type. [online]. 2009. Vol. 430, no. 1, p. 251–270. [Accessed 5 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.laa.2008.07.013 Copy citation