Let $X$ be a smooth algebraic curve over $\mathbb C$, and let $F$ be a vector bundle on it of degree $1$, take the dual of an extention $$0\rightarrow F^*\rightarrow E\rightarrow F\rightarrow0$$ is again an extension of $F$ by $F^*$, my questions are:
How can I explicitly describe this involution on vector space $Ext^1(F,F^*)$?
Are there any criterian for $E$ to be stable? ($F$ is taken to be semistable)
Thanks