  We consider a new matrix model based on the simply connected compact
exceptional Lie group E6. A matrix Chern-Simons theory is directly derived from
the invariant on E6. It is stated that the similar argument as Smolin which
derives an effective action of the matrix string type can also be held in our
model. An important difference is that our model has twice as many degrees of
freedom as Smolin's model has. One way to introduce the cosmological term is
the compactification on directions. It is of great interest that the properties
of the product space $\Vec{\mathfrak{J}^c} \times \Vec{\mathcal{G}}$, in which
the degrees of freedom of our model live, are very similar to those of the
physical Hilbert space.
