Generalized quadrangles and subconstituent algebra




The point graph of a generalized quadrangle GQ(s, t) is a strongly regular graph Γ = srg(ν, κ, λ, 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 T × â„‚X → â„‚X we find the decomposition into irreducible T-submodules of â„‚X (where X is the set of vertices of the Γ).


strongly regular graphs , generalized quadrangles , Terwilliger algebra
  • Fernando Levstein FaMAF-CIEM,UNC, Universidad Nacional de Córdoba Medina Allende y Haya de la Torre. CP 5000 - Córdoba, Argentina.
  • Carolina Maldonado Departamento de Matemática, Centro de Ciências Exatas e da Natureza, Universidade Federal de Pernambuco Av. Prof. Luiz Freire, s/n Cidade Universitária - Recife, Brasil.
  • Pages: 53–75
  • Date Published: 2010-06-01
  • Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal


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How to Cite

F. Levstein and C. Maldonado, “Generalized quadrangles and subconstituent algebra”, CUBO, vol. 12, no. 2, pp. 53–75, Jun. 2010.