  Let $W$ denote a simply-laced Coxeter group with $n$ generators. We construct
an $n$-dimensional 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 find that the kernel of $\phi$ is
the center $Z(W)$ of $W.$
