Supersymmetric BKP systems and their symmetries

Abstract

In this paper, we construct the additional symmetries of the supersymmetric BKP(SBKP) hierarchy. These additional flows constitute a B type $S{W}_{1+\infty }$ 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 $S{W}_{1+\infty }⨁S{W}_{1+\infty }$ 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 $N=2$ supersymmetric Block type symmetry.

arXiv comment22 Pages, Nuclear Physics B 896(2015) 716-737

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Cited by in corpus (7)

• Gauge transformation and symmetries of the commutative multi-component BKP hierarchy
• Bilinear equations in Darboux transformations by Boson-Fermion correspondence
• Quantum torus symmetries of multicomponent modified KP hierarchy and reductions
• Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries
• Quantum Torus symmetries of the CKP and multi-component CKP hierarchies
• Constrained lattice-field hierarchies and Toda system with Block symmetry
• Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy