CONICET | Buscador de Institutos y Recursos Humanos

The point graph of a generalized quadrangle $GQ(s,t)$ is astrongly regular graph $Gamma=srg( u,kappa, lambda, mu)$whose parameters depend on $s$ and $t$. By a detailed analysis ofthe adjacency matrix we compute the Terwilliger algebra of thiskind of graphs (and denoted it by $mathcal{T}$). We find that there are only two non-isomorphicTerwilliger algebras for all the generalized quadrangles. Thetwo classes correspond to wether $s^2=t$ or not. We decompose thealgebra into direct sum of simple ideals. Considering the action$mathcal{T} imes mathbb{C}^X longrightarrow mathbb{C}^X$ wefind the decomposition into irreducible $mathcal{T}$-submodulesof $mathbb{C}^X$ (where $X$ is the set of vertices of the$Gamma$).