  We investigate the spectral flows of the hermitian Wilson-Dirac operator in
the fundamental and adjoint representations on two ensembles of pure SU(2)
gauge field configurations at the same physical volume. We find several
background gauge field configurations where the index of the hermitian
Wilson-Dirac operator in the adjoint representation is not four times the index
in the fundamental representation. This could imply a topological basis for the
existence of degenerate vacua in supersymmetric Yang-Mills theories.
