On the Gieseker Harder-Narasimhan filtration for principal bundles
  We give an example of an orthogonal bundle where the Harder-Narasimhan filtration, with respect to Gieseker semistability, of its underlying vector bundle does not correspond to any parabolic reduction of the orthogonal bundle. A similar example is given for the symplectic case. 
Indranil Biswas and Alfonso Zamora
math.AG