an embedding of $Gl(V)/P$ inside a projective space $\mathbb {P}(W)$.\
Now let $\pi:E \rightarrow X$ a principal $G$ -bundle on $X$. Let $E(G)$ be the associated group scheme over $X$. Let $E(Gl(V)/P)$ be the associated fiber space. Let $T_\pi$ denote the relative tangent bundle on $E(Gl(V)/P)$. Let $E(\mathcal L)$ be the associated line bundle on $E(Gl(V)/P$ corresponding the line bundle $\mathcal L$ on $Sl(V)/P$. The group scheme $E(G)$ acts on $E(G/P)$. Let $E(G)_\circ$ be the generic fiber of $E(G)$. It is a group scheme defined over the function field of $X$. $E(G)_\circ$ acts on $E(Gl(V)/P)_\circ$ which is linearized by $E(\mathcal L)_\circ$. Let suppose $\sigma$ be a reduction of the induced $Gl(V)$-bundle to $P$. Then corresponding to this reduction we get a section of (called $\sigma$ again) of $E(Gl(V)/P)$ over $X$. Let $\sigma_\circ$ be the associated $k(X)$-valued point of $E(Gl(V)/P_\circ)$. Suppose $\sigma_\circ$ is a non-semistable point for the action of $E(G)_\circ$ on $E(Gl(V)/P)$. Let $P(\sigma_\circ)$ denote the instability parabolic associated to the point $\sigma_\circ$. We call $P(\sigma_\circ)$ the instability parabolic corresponding to this reduction. Let $T_\sigma$ denote the pullback of $T_\pi$ via the section $\sigma$.

(See \[RR, Proposition 3.10, (1)\]) Let $\sigma_\circ$ be a semistable point for the action of $E(G)_\circ$ 