the connected component of the centre of $G$ to that of $Gl(V)$. If the characteristic $k$ is zero and $E$ is a semistable $G$-bundle on $X$ then the induced $Gl(V)$-bundle is also semistable. From this it follows easily that if the characteristic of the field is sufficiently large , then again a semistable $G$-bundle induces a semistable $Gl(V)$-bundle. This is quantified in \[IMP\] where in it is shown that if char $k >$ ht $(\rho)$, then a semistable $G$-bundle induce a semistable $Gl(V)$-bundle on extension of structure group. In positive characteristic however, it is in not in general true that a semistable $G$ bundle will induce a semistable $Gl(V)$-bundle. A principal $G$-bundle on $X$ is said to be strongly semistable if all its frobenius pullbacks are semistable. In char 0, the frobenius map is just identity and hence the notion of semistability and strong semistability coincide. In Ramanan-Ramanathan \[RR\], it is shown that a strongly semistable $G$-bundle induces a strongly semistable $Gl(V)$-bundle. This result is sharpened in the paper of Coiai-Holla \[CH\] where the authors show that given a representation $\rho$ as before, there exists a non-negative integer $t$ such that if $E$ is any $G$-bundle on $X$ which along 