Additional Symmetries of Supersymmetric KP Hierarchies

Abstract

We investigate the additional symmetries of several supersymmetric KP hierarchies: the SKP hierarchy of Manin and Radul, the ${SKP}_2$ hierarchy, and the Jacobian SKP hierarchy. In all three cases we find that the algebra of symmetries is isomorphic to the algebra of superdifferential operators, or equivalently $\SW_{1+\infty}$. These results seem to suggest that despite their realization depending on the dynamics, the additional symmetries are kinematical in nature.

21 pages, Plain TeX, BONN-HE-93-31

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Cited by in corpus (8)

• Darboux Transformation for the Manin-Radul Supersymmetric KdV equation
• Supersymmetric KP Hierarchy: ``Ghost'' Symmetry Structure, Reductions and Darboux-Backlund Solutions
• Supersymmetric BKP systems and their symmetries
• N=2 local and N=4 nonlocal reductions of supersymmetric KP hierarchy in N=2 superspace
• Symmetries of Supersymmetric Integrable Hierarchies of KP Type
• Darboux Transformations for SUSY Integrable Systems
• Supersymmetric KP hierarchy in N=1 superspace and its N=2 reductions
• Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy