Generalized quadrangles and subconstituent algebra
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Fernando Levstein
levstein@famaf.unc.edu.ar
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Carolina Maldonado
cmaldona@famaf.unc.edu.ar
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DOI:
https://doi.org/10.4067/S0719-06462010000200005Abstract
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).
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