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Title:Leonard triples and hypercubes
Authors:ID Miklavič, Štefko (Author)
Files:URL http://dx.doi.org/10.1007/s10801-007-0108-x
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract:Let V denote a vector space over C with finite positive dimension. By a Leonard triple on V we mean an ordered triple of linear operators on V such that for each of these operators there exists a basis of V with respect to which the matrix representing that operator is diagonal and the matrices representing the other two operators are irreducible tridiagonal. Let D denote a positive integer and let QD denote the graph of the D-dimensional hypercube. Let X$denotethevertexsetof$QD and let AMatX(C) denote the adjacency matrix of QD. Fix xX and let AMatX(C) denote the corresponding dual adjacency matrix. Let T denote the subalgebra of MatX(C)$generatedby$A,A. We refer to T as the Terwilliger algebra of QD with respect to x. The matrices A and A are related by the fact that 2iA=AAεAεA and 2iA=AεAAAε, where 2iAε=AAAA and i2=1. We show that the triple A, A, Aε acts on each irreducible T-module as a Leonard triple. We give a detailed description of these Leonard triples.
Keywords:mathematics, graph theory, Leonard triple, distance-regular graph, hypercube, Terwilliger algebra
Year of publishing:2007
Number of pages:str. 397-424
Numbering:Vol. 28, no. 3
PID:20.500.12556/RUP-1597 This link opens in a new window
ISSN:0925-9899
UDC:519.17
COBISS.SI-ID:14624857 This link opens in a new window
Publication date in RUP:15.10.2013
Views:5607
Downloads:124
Metadata:XML DC-XML DC-RDF
:
MIKLAVIČ, Štefko, 2007, Leonard triples and hypercubes. [online]. 2007. Vol. 28, no. 3, p. 397–424. [Accessed 17 March 2025]. Retrieved from: http://dx.doi.org/10.1007/s10801-007-0108-x
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Secondary language

Language:English
Keywords:matematika, teorija grafov, razdaljno regularni grafi, Leonardova trojica, hiperkocka, Terwilligerjeva algebra


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