Abstract:
 Let W denote a simplylaced Coxeter group with n generators. We construct an ndimensional representation $\phi$ of W over the finite field $F_2$ of two elements. The action of $\phi(W)$ on $F_2^n$ by left multiplication is corresponding to a combinatorial structure extracted and generalized from Vogan diagrams. In each case W of types A; D and E; we determine the orbits of $F_2^n$ under the action of $\phi(W)$, and conclude that the kernel of $\phi$ is the center Z(W) of W.
