Abstract
In this paper, we construct the additional symmetries of the supersymmetric BKP (SBKP) hierarchy. These additional flows constitute a B type 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+∞ 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.
Highlights
In the study of integrable hierarchies, it is interesting to find their symmetries and identify the algebraic structure of the symmetries
Our earlier papers show that the Block type algebras appear in Toda type difference systems and in differential systems such as two-BKP hierarchy, D type Drinfeld-Sokolov hierarchy [26]
The above results show that in their corresponding supersymmetric systems, there exists the hidden N = 2 Block type supersymmetric algebraic structures. These results further show that the Block type infinite dimensional Lie algebra has a certain of universality in integrable hierarchies
Summary
In the study of integrable hierarchies, it is interesting to find their symmetries and identify the algebraic structure of the symmetries. As a reduction of the S2BKP hierarchy, in this paper a new supersymmetric Drinfeld-Sokolov hierarchy of type D will be constructed and proved to have a super Block type additional symmetry. Toda lattice equations are interesting integrable nonlinear systems in connection with conformal field theories Their Virasoro symmetry can be extended to a Wn algebra which is known to arise from the Hamiltonian structure of the generalized KdV equation [34] by incorporating conserved currents of higher spins. As a Bosonic reduction of the supersymmetric two-component BKP hierarchy, we define a new constrained system called the supersymmetric Drinfeld-Sokolov hierarchy of type D which possesses a N = 2 supersymmetric Block type Lie algebra in the following two sections. We will give a short conclusion and a further discussion
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