Convexes divisibles II

A properly convex open cone in ℝm is called divisible if there exists a discrete subgroup Γ of GLℝm preserving C such that the quotient Γ is compact. We describe the Zariski closure of such a group Γ. We show that if C is divisible but is neither a product nor a symmetric cone, then Γ is Zariski dense in GLℝm.