Generalized quadrangles and subconstituent algebra ¹

The point graph of a generalized quadrangle GQ (s, t) is a strongly regular graph G = srg( ?, ?, ?, μ) whose parameters depend on s and t. By a detailed analysis of the adjacency matrix we compute the Terwilliger algebra of this kind of graphs (and denoted it by T ). We find that there are...

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Autores principales:	Levstein,Fernando, Maldonado,Carolina
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2010
Materias:	strongly regular graphs neralized quadrangles Terwilliger algebra
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000200005
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spelling	oai:scielo:S0719-064620100002000052018-10-08Generalized quadrangles and subconstituent algebra ¹Levstein,FernandoMaldonado,Carolina strongly regular graphs neralized quadrangles Terwilliger algebra The point graph of a generalized quadrangle GQ (s, t) is a strongly regular graph G = srg( ?, ?, ?, μ) whose parameters depend on s and t. By a detailed analysis of the adjacency matrix we compute the Terwilliger algebra of this kind of graphs (and denoted it by T ). We find that there are only two non-isomorphic Terwilliger algebras for all the generalized quadrangles. The two classes correspond to wether s² = t or not. We decompose the algebra into direct sum of simple ideals. Considering the action ? × Cx→ Cx we find the decomposition into irreducible T -submodules of Cx (where X is the set of vertices of the G ).info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.12 n.2 20102010-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000200005en10.4067/S0719-06462010000200005
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	strongly regular graphs neralized quadrangles Terwilliger algebra
spellingShingle	strongly regular graphs neralized quadrangles Terwilliger algebra Levstein,Fernando Maldonado,Carolina Generalized quadrangles and subconstituent algebra ¹
description	The point graph of a generalized quadrangle GQ (s, t) is a strongly regular graph G = srg( ?, ?, ?, μ) whose parameters depend on s and t. By a detailed analysis of the adjacency matrix we compute the Terwilliger algebra of this kind of graphs (and denoted it by T ). We find that there are only two non-isomorphic Terwilliger algebras for all the generalized quadrangles. The two classes correspond to wether s² = t or not. We decompose the algebra into direct sum of simple ideals. Considering the action ? × Cx→ Cx we find the decomposition into irreducible T -submodules of Cx (where X is the set of vertices of the G ).
author	Levstein,Fernando Maldonado,Carolina
author_facet	Levstein,Fernando Maldonado,Carolina
author_sort	Levstein,Fernando
title	Generalized quadrangles and subconstituent algebra ¹
title_short	Generalized quadrangles and subconstituent algebra ¹
title_full	Generalized quadrangles and subconstituent algebra ¹
title_fullStr	Generalized quadrangles and subconstituent algebra ¹
title_full_unstemmed	Generalized quadrangles and subconstituent algebra ¹
title_sort	generalized quadrangles and subconstituent algebra ¹
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2010
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000200005
work_keys_str_mv	AT levsteinfernando generalizedquadranglesandsubconstituentalgebra1 AT maldonadocarolina generalizedquadranglesandsubconstituentalgebra1
_version_	1714206765528121344

Generalized quadrangles and subconstituent algebra ¹

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