Supersymmetric BKP systems and their symmetries

In this paper, we construct the additional symmetries of the supersymmetric BKP (SBKP) hierarchy. These additional flows constitute a B type SW1+∞SW1+∞ Lie algebra because of the B type reduction of the supersymmetric BKP hierarchy. Further we generalize the SBKP hierarchy to a supersymmetric two-component BKP (S2BKP) hierarchy equipped with a B type SW1+∞⨁SW1+∞SW1+∞⨁SW1+∞ Lie algebra. As a bosonic reduction of the S2BKP hierarchy, we define a new constrained system called the supersymmetric Drinfeld–Sokolov hierarchy of type D which admits a N=2N=2 supersymmetric Block type symmetry.