Abstract

LEVSTEIN, Fernando  and  MALDONADO, Carolina. Generalized quadrangles and subconstituent algebra ¹. Cubo [online]. 2010, vol.12, n.2, pp. 53-75. ISSN 0719-0646.  doi: 10.4067/S0719-06462010000200005.

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 ? × C^x→ C^x we find the decomposition into irreducible T -submodules of C^x (where X is the set of vertices of the G ).

Keywords : strongly regular graphs; neralized quadrangles; Terwilliger algebra.