Let $E$ be a vector bundle of rank $r$ and degree $d$ over a smooth curve $X$. Is there any canonical exact sequence for $Sym^k(E)$? in particular what is the degree of $Sym^k(E)$?
Suppose $E$ is stable, is $Sym^k(E)$ is stable ? Is there any interesting information about $Sym^k(E)$?
Thanks