Bosonic Symmetries of the Extended Fermionic (2N, 2M)-Toda Hierarchy

Abstract

We construct the additional symmetries of the fermionic (2N, 2M)-Toda hierarchy based on a generalization of the N=(1∣1) supersymmetric two-dimensional Toda lattice hierarchy. These additional flows constitute a w_∞×w_∞ 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 that admits a bosonic Block-type superconformal structure.