Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy

Abstract

In this paper, we construct the additional symmetries of the fermionic $(2N,2M)$-Toda hierarchy basing on the generalization of the $N=(1|1)$ supersymmetric two dimensional Toda lattice hierarchy. These additional flows constitute a $w_{\infty }\times w_{\infty }$ Lie algebra. As a Bosonic reduction of the $N=(1|1)$ supersymmetric two dimensional Toda lattice hierarchy and the fermionic $(2N,2M)$-Toda hierarchy, we define a new extended fermionic $(2N,2M)$-Toda hierarchy which admits a Bosonic Block type superconformal structure.

17 pages

References in corpus (6)

• The Extended Bigraded Toda hierarchy
• Solutions of bigraded Toda hierarchy
• Supersymmetric BKP systems and their symmetries
• Quantum Torus symmetry of the KP, KdV and BKP hierarchies
• Constrained lattice-field hierarchies and Toda system with Block symmetry
• N=(1|1) supersymmetric dispersionless Toda lattice hierarchy

Cited by in corpus (1)

• Darboux transformations and Fay identities for the extended bigraded Toda hierarchy