Stability of symmetric powers of vector bundles of rank two with even degree on a curve

This paper treats the strict semi-stability of symmetric powers [Formula: see text] a stable vector bundle rank with even degree on smooth projective curve genus text]. The is equivalent to orthogonality or existence bisection ruled surface whose self-intersection number zero. A relation between two interpretations investigated in this through elementary transformations. also gives classification strictly semi-stable Moreover, it shown that when stable, every power for all but finite moduli bundles fixed determinant