  Let H_1=SL(5), H_2=SL(3), H=H_1 \times H_2. It is known that (G,V) is a
prehomogeneous vector space (see [22], [26], [25], for the definition of
prehomogeneous vector spaces). A non-constant polynomial \delta(x) on V is
called a relative invariant polynomial if there exists a character \chi such
that \delta(gx)=\chi(g)\delta(x). Such \delta(x) exists for our case and is
essentially unique. So we define V^{ss}={x in V such that \delta(x) is not
equal to 0}. For x in V_R^{ss}, let H_{x R+}^0 be the connected component of 1
in classical topology of the stabilizer H_{x R}. We will prove that if x in
V_R^ss is "sufficiently irrational", H_{x R+}^0 H_Z is dense in H_R.
